Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other m...Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.展开更多
In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys....In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285(2015),265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme(UGKS),we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30(2008),1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.展开更多
The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredient...The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by parts.In this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation.The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions.Several numerical experiments are reported which show the good behavior of the method.展开更多
Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of...Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.展开更多
An accurate and rapid method for solving radiative transfer equation is presented in this paper. According to the fact that the multiple scattering component of radiance is less sensitive to the error of phase functio...An accurate and rapid method for solving radiative transfer equation is presented in this paper. According to the fact that the multiple scattering component of radiance is less sensitive to the error of phase function than the single scattering component is,we calculate the multiple scattering component by using delta-Eddington approximation and the single scattering component by solving radiative transfer equation. On the ground, when multiple sattering component is small, for example, when the total optical depth T is small, the accurate radiance can be obtained with this method. For the need of the space remote sensing, the upward radiance at the top of the atmosphere is mainly studied, and an approximate expression is presented to correct the multiple scattering component. Compared with the more precise Gauss-Seidel method.the results from this method show an accuracy of better than 10% when zenith angle 0 < 50 掳 and T < 1. The computational speed of this method is, however, much faster than that of Gauss-Seidel method.展开更多
This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem ...This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Galerkin method is developed. Since specular reflection is considered on borders, a very accurate algorithm has been developed for calculation of partition ratio coefficients of incident solid angles to the several reflected solid angles. The developed algorithms are tested on a paraboloid-shaped geometry used for example on concentrated solar power technologies.展开更多
Accurate estimates of albedos are required in climate modeling. Accurate and simple schemes for radiative transfer within canopy are required for these estimates, but severe limitations exist. This paper developed a f...Accurate estimates of albedos are required in climate modeling. Accurate and simple schemes for radiative transfer within canopy are required for these estimates, but severe limitations exist. This paper developed a four-stream solar radiative transfer model and coupled it with a land surface process model. The radiative model uses a four-stream approximation method as in the atmosphere to obtain analytic solutions of the basic equation of canopy radiative transfer. As an analytical model, the four-stream radiative transfer model can be easily applied efficiently to improve the parameterization of land surface radiation in climate models. Our four-stream solar radiative transfer model is based on a two-stream short wave radiative transfer model. It can simulate short wave solar radiative transfer within canopy according to the relevant theory in the atmosphere. Each parameter of the basic radiative transfer equation of canopy has special geometry and optical characters of leaves or canopy. The upward or downward radiative fluxes are related to the diffuse phase function, the G-function, leaf reflectivity and transmission, leaf area index, and the solar angle of the incident beam. The four-stream simulation is compared with that of the two-stream model. The four-stream model is proved successful through its consistent modeling of canopy albedo at any solar incident angle. In order to compare and find differences between the results predicted by the four- and two-stream models, a number of numerical experiments are performed through examining the effects of different leaf area indices, leaf angle distributions, optical properties of leaves, and ground surface conditions on the canopy albedo. Parallel experiments show that the canopy albedos predicted by the two models differ significantly when the leaf angle distribution is spherical and vertical. The results also show that the difference is particularly great for different incident solar beams. One additional experiment is carried out to evaluate the simulations of the BATS land surface model coupled with the two- and four-stream radiative transfer models. Station observations in 1998 are used for comparison. The results indicate that the simulation of BATS coupled with the four-stream model is the best because the surface absorbed solar radiation from the four-stream model is the closest to the observation.展开更多
In this work,a discrete unified gas kinetic scheme(DUGKS)is developed for radiative transfer in anisotropic scattering media.The method is an extension of a previous one for isotropic radiation problems[1].The present...In this work,a discrete unified gas kinetic scheme(DUGKS)is developed for radiative transfer in anisotropic scattering media.The method is an extension of a previous one for isotropic radiation problems[1].The present scheme is a finite-volume discretization of the anisotropic gray radiation equation,where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion.With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces,the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime.Several one-and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS,and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.展开更多
In the bioluminescence tomography (BLT) problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal's body surface. The BLT probl...In the bioluminescence tomography (BLT) problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal's body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method (CCBM) based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation (RTE). By properly adjusting the parameter in the Robin boundary condition, we achieve one important property: the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.展开更多
We proposed a wide spectrum and rapid calculation model FALTRAN( Fast Atmospheric Limb TRANsmission),to solve the problems of current radiative transfer model in limb remote sensing. In FALTRAN:( 1) Band model algorit...We proposed a wide spectrum and rapid calculation model FALTRAN( Fast Atmospheric Limb TRANsmission),to solve the problems of current radiative transfer model in limb remote sensing. In FALTRAN:( 1) Band model algorithm was employed and the molecular spectroscopy database was based on HITRAN2008.( 2) Limb radiative transfer equation consists of scattering and thermal radiation was established,and according to the limb geometry characteristic,a Hemisphere Radiation Adding( HRA) approach based on finite difference method was proposed to solve it. We investigated the atmospheric limb radiations under typical atmospheric modes in several commonly used remote sensing bands. Moreover,radiation contribution by two hemispheres was quantitative analyzed as well. Validation results show that the relative differences between FALTRAN and Combining Differential-Integral( CDI) model are within 2%,and calculation results by FALTRAN have good agreement with Michelson Interferometer for Passive Atmospheric Sounding( MIPAS) measurements. FALTRAN is proven to be reliable in the limb radiative transfer calculation.展开更多
Calculation of the net radiation emitted by a CH4-Ar mixture, in a temperature range of 5,000-30,000 K with the assumption of local thermodynamic equilibrium (LTE), is conducted. Continuum and line emissions are tak...Calculation of the net radiation emitted by a CH4-Ar mixture, in a temperature range of 5,000-30,000 K with the assumption of local thermodynamic equilibrium (LTE), is conducted. Continuum and line emissions are taken into account. The radiative transfer of each line is calculated by means of an escape factor depending on the shape and broadening of the line. Assuming a cylindrical, homogeneous, and isothermal plasma, the net emission coefficient is calculated for different pressures between 1 atm and 10 atm and arc radia of 0 mm to 1 mm. Results show that the argon presence in the CH4-Ar mixture has a significant effect on the total radiation emitted for the temperature above 17,000 K and the results for pure argon agree with those of BAUDER and EVANS.展开更多
It is well acknowledged that the equation of radiative transfer(ERT)provides an accurate prediction of light propagation in biological tissues,while the diffusion approximation(DA)is of limited accuracy for the transp...It is well acknowledged that the equation of radiative transfer(ERT)provides an accurate prediction of light propagation in biological tissues,while the diffusion approximation(DA)is of limited accuracy for the transport regime.However,ERT-based reconstruction codes require much longer computation times as compared to DA-based reconstruction codes.We introduce here a computationally efficient algorithm,called a diffusion–transport hybrid solver,that makes use of the DA-or low-order ERT-based inverse solution as an initial guess for the full ERT-based reconstruction solution.To evaluate the performance of this hybrid method,we present extensive studies involving numerical tissue phantoms and experimental data.As a result,we show that the hybrid method reduces the reconstruction time by a factor of up to 23,depending on the physical character of the problem.展开更多
Bioluminescence imaging is a kind of emerging detection technology at cellular,molecular and genetic level.The most popular bioluminescence imaging model is diffusion approximation(DA).However,because of the ill-posed...Bioluminescence imaging is a kind of emerging detection technology at cellular,molecular and genetic level.The most popular bioluminescence imaging model is diffusion approximation(DA).However,because of the ill-posedness of the DA-based inverse problem and the instability of reconstruction algorithms,the location accuracy of the reconstructed sources is low.Radiative transfer equation(RTE),which considers the direction of the photon migration and the effect of absorption and scattering in tissues,can accurately express the transmission of bioluminescent photons through the tissues.In this paper,we studied the bioluminescence imaging based on the RTE.2D simulations were performed,and quantitative evaluation was given by the absolute source position error,the relative source area error and the minimum bounding box.The results of the experiment showed that the imaging quality based on RTE was better than that one based on DA.展开更多
Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational ax-isymmetric dusty gas, which has a variable azimuthal and axia...Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational ax-isymmetric dusty gas, which has a variable azimuthal and axial fluid velocity. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equi-librium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. The fluid velocities in the ambient medium are assumed to obey exponential laws. The shock wave moves with variable velocity. The effects of variation of the mass concentration of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times. Also, a comparison between the solutions in the cases of isothermal and adia-batic flows is made.展开更多
Prediction of the coupled conduction-radiation heat transfer in composite materials with periodic structure is important in high-temperature applications of the materials. The temperature dependence of thermal propert...Prediction of the coupled conduction-radiation heat transfer in composite materials with periodic structure is important in high-temperature applications of the materials. The temperature dependence of thermal properties complicates the problem. In this work, a multiscale model is proposed for the conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties. Homogenization analysis of the coupled conduction and radiative transfer equations is conducted, in which the temperature dependence of thermal properties is considered. Both the macroscopic homogenized equations and the local unit cell problems are derived. It is proved that the macroscopic average temperature can be used in the unit cell problems for the first-order corrections of the temperature and radiative intensity, and the calculations of effective thermal properties. The temperature dependence of thermal properties only influences the higher-order corrections. A multiscale numerical method is proposed based on the analysis. The Gaussian process (GP) regression is coupled into the multiscale algorithm to build a correlation between thermal properties and temperature for the macroscale iterations and prevent the repetitive solving of unit cell problems. The GP model is updated by additional solutions of unit cell problems during the iteration according to a variance threshold. Numerical simulations of conduction-radiation heat transfer in composite with isotropic and anisotropic periodic structures are used to validate the proposed multiscale model. It is found that the accuracy and efficiency of the multiscale method can be guaranteed by using a proper variance threshold for the GP model. The multiscale model can provide both the average temperature and radiative intensity fields and their detailed fluctuations due to the local structures.展开更多
In this paper,we propose a machine learning approach via model-operatordata network(MOD-Net)for solving PDEs.A MOD-Net is driven by a model to solve PDEs based on operator representationwith regularization fromdata.Fo...In this paper,we propose a machine learning approach via model-operatordata network(MOD-Net)for solving PDEs.A MOD-Net is driven by a model to solve PDEs based on operator representationwith regularization fromdata.For linear PDEs,we use a DNN to parameterize the Green’s function and obtain the neural operator to approximate the solution according to the Green’s method.To train the DNN,the empirical risk consists of the mean squared loss with the least square formulation or the variational formulation of the governing equation and boundary conditions.For complicated problems,the empirical risk also includes a fewlabels,which are computed on coarse grid points with cheap computation cost and significantly improves the model accuracy.Intuitively,the labeled dataset works as a regularization in addition to the model constraints.The MOD-Net solves a family of PDEs rather than a specific one and is much more efficient than original neural operator because few expensive labels are required.We numerically show MOD-Net is very efficient in solving Poisson equation and one-dimensional radiative transfer equation.For nonlinear PDEs,the nonlinear MOD-Net can be similarly used as an ansatz for solving nonlinear PDEs,exemplified by solving several nonlinear PDE problems,such as the Burgers equation.展开更多
The present work concerns the numerical approximation of the M_(1) model for radiative transfer.The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws ...The present work concerns the numerical approximation of the M_(1) model for radiative transfer.The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this model.We propose to derive an HLLC method which preserves the stationary contact waves.To supplement this essential property,the method is proved to be robust and to preserve the physical admissible states.Next,a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical regimes.The relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.展开更多
文摘Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.
基金supported by the Science and Technology Development foundation of China Academy of Engineering Physics(Grant Nos.2015B0202041,2015B0202040)the Science and Technology Development foundation of China Academy of Engineering Physics(Grant 2015B0202040)+2 种基金the Science and Technology Development foundation of China Academy of Engineering Physics(Grant No.2015B0202033)for LiNSFC(Grant No.11371068)for SunNSFC(Grant No.11371068)for Zeng
文摘In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285(2015),265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme(UGKS),we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30(2008),1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.
文摘The discrete duality finite volume method has proven to be a practical tool for discretizing partial differential equations coming from a wide variety of areas of physics on nearly arbitrary meshes.The main ingredients of the method are:(1)use of three meshes,(2)use of the Gauss-Green theorem for the approximation of derivatives,(3)discrete integration by parts.In this article we propose to extend this method to the coupled grey thermal-P_(N) radiative transfer equations in Cartesian and cylindrical coordinates in order to be able to deal with two-dimensional Lagrangian approximations of the interaction of matter with radiation.The stability under a Courant-Friedrichs-Lewy condition and the preservation of the diffusion asymptotic limit are proved while the experimental second-order accuracy is observed with manufactured solutions.Several numerical experiments are reported which show the good behavior of the method.
文摘Linearization of Radiative Transfer Equation (RTE) is the key step in physical retrieval of atmospheric temperature and moisture profiles from InfRared (IR) sounder observations. In this paper, the successive forms of temperature and water vapor mixing ratio component weighting functions are derived by applying one term variation method to RTE with surface emissivity and solar reflectivity contained. Retrivals of temperature and water vapor mixing ratio profiles from simulated Atmospheric Infrared Sounder (AIRS) observations with surface emissivity and solar reflectivity are presented.
文摘An accurate and rapid method for solving radiative transfer equation is presented in this paper. According to the fact that the multiple scattering component of radiance is less sensitive to the error of phase function than the single scattering component is,we calculate the multiple scattering component by using delta-Eddington approximation and the single scattering component by solving radiative transfer equation. On the ground, when multiple sattering component is small, for example, when the total optical depth T is small, the accurate radiance can be obtained with this method. For the need of the space remote sensing, the upward radiance at the top of the atmosphere is mainly studied, and an approximate expression is presented to correct the multiple scattering component. Compared with the more precise Gauss-Seidel method.the results from this method show an accuracy of better than 10% when zenith angle 0 < 50 掳 and T < 1. The computational speed of this method is, however, much faster than that of Gauss-Seidel method.
文摘This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Galerkin method is developed. Since specular reflection is considered on borders, a very accurate algorithm has been developed for calculation of partition ratio coefficients of incident solid angles to the several reflected solid angles. The developed algorithms are tested on a paraboloid-shaped geometry used for example on concentrated solar power technologies.
基金Supported by the National Natural Science Foundation of China under Grant Nos.40375026 and 40233034.
文摘Accurate estimates of albedos are required in climate modeling. Accurate and simple schemes for radiative transfer within canopy are required for these estimates, but severe limitations exist. This paper developed a four-stream solar radiative transfer model and coupled it with a land surface process model. The radiative model uses a four-stream approximation method as in the atmosphere to obtain analytic solutions of the basic equation of canopy radiative transfer. As an analytical model, the four-stream radiative transfer model can be easily applied efficiently to improve the parameterization of land surface radiation in climate models. Our four-stream solar radiative transfer model is based on a two-stream short wave radiative transfer model. It can simulate short wave solar radiative transfer within canopy according to the relevant theory in the atmosphere. Each parameter of the basic radiative transfer equation of canopy has special geometry and optical characters of leaves or canopy. The upward or downward radiative fluxes are related to the diffuse phase function, the G-function, leaf reflectivity and transmission, leaf area index, and the solar angle of the incident beam. The four-stream simulation is compared with that of the two-stream model. The four-stream model is proved successful through its consistent modeling of canopy albedo at any solar incident angle. In order to compare and find differences between the results predicted by the four- and two-stream models, a number of numerical experiments are performed through examining the effects of different leaf area indices, leaf angle distributions, optical properties of leaves, and ground surface conditions on the canopy albedo. Parallel experiments show that the canopy albedos predicted by the two models differ significantly when the leaf angle distribution is spherical and vertical. The results also show that the difference is particularly great for different incident solar beams. One additional experiment is carried out to evaluate the simulations of the BATS land surface model coupled with the two- and four-stream radiative transfer models. Station observations in 1998 are used for comparison. The results indicate that the simulation of BATS coupled with the four-stream model is the best because the surface absorbed solar radiation from the four-stream model is the closest to the observation.
基金The National Key R&D Program of China(No.2018YFE0180900)the Fundamental Research Funds for the Central Universities(No.2019kfyXMBZ040).
文摘In this work,a discrete unified gas kinetic scheme(DUGKS)is developed for radiative transfer in anisotropic scattering media.The method is an extension of a previous one for isotropic radiation problems[1].The present scheme is a finite-volume discretization of the anisotropic gray radiation equation,where the anisotropic scattering phase function is approximated by the Legendre polynomial expansion.With the coupling of free transport and scattering processes in the reconstruction of the flux at cell interfaces,the present DUGKS has the nice unified preserving properties such that the cell size is not limited by the photon mean free path even in the optical thick regime.Several one-and two-dimensional numerical tests are conducted to validate the performance of the present DUGKS,and the numerical results demonstrate that the scheme is a reliable method for anisotropic radiative heat transfer problems.
文摘In the bioluminescence tomography (BLT) problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal's body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method (CCBM) based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation (RTE). By properly adjusting the parameter in the Robin boundary condition, we achieve one important property: the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.
基金National Natural Science Foundation of China(No.11173008)Fundamental Research Funds for the Central Universities(No.103.1.2E022050205)
文摘We proposed a wide spectrum and rapid calculation model FALTRAN( Fast Atmospheric Limb TRANsmission),to solve the problems of current radiative transfer model in limb remote sensing. In FALTRAN:( 1) Band model algorithm was employed and the molecular spectroscopy database was based on HITRAN2008.( 2) Limb radiative transfer equation consists of scattering and thermal radiation was established,and according to the limb geometry characteristic,a Hemisphere Radiation Adding( HRA) approach based on finite difference method was proposed to solve it. We investigated the atmospheric limb radiations under typical atmospheric modes in several commonly used remote sensing bands. Moreover,radiation contribution by two hemispheres was quantitative analyzed as well. Validation results show that the relative differences between FALTRAN and Combining Differential-Integral( CDI) model are within 2%,and calculation results by FALTRAN have good agreement with Michelson Interferometer for Passive Atmospheric Sounding( MIPAS) measurements. FALTRAN is proven to be reliable in the limb radiative transfer calculation.
文摘Calculation of the net radiation emitted by a CH4-Ar mixture, in a temperature range of 5,000-30,000 K with the assumption of local thermodynamic equilibrium (LTE), is conducted. Continuum and line emissions are taken into account. The radiative transfer of each line is calculated by means of an escape factor depending on the shape and broadening of the line. Assuming a cylindrical, homogeneous, and isothermal plasma, the net emission coefficient is calculated for different pressures between 1 atm and 10 atm and arc radia of 0 mm to 1 mm. Results show that the argon presence in the CH4-Ar mixture has a significant effect on the total radiation emitted for the temperature above 17,000 K and the results for pure argon agree with those of BAUDER and EVANS.
基金supported in part by grants from the National Cancer Institute(NCI)(4R33CA118666“Small animal tomography system for green fluorescent protein imaging”and 5U54CA126513-03“Tumor Microenvironment Network—The role of inflammation and stroma in digestive cancer”)the National Institute for Arthritis and Musculoskeletal and Skin Diseases(NIAMS)(2R01AR46255“Optical tomographic imaging of joint diseases”),which are both part of the National Institutes of Health(NIH).
文摘It is well acknowledged that the equation of radiative transfer(ERT)provides an accurate prediction of light propagation in biological tissues,while the diffusion approximation(DA)is of limited accuracy for the transport regime.However,ERT-based reconstruction codes require much longer computation times as compared to DA-based reconstruction codes.We introduce here a computationally efficient algorithm,called a diffusion–transport hybrid solver,that makes use of the DA-or low-order ERT-based inverse solution as an initial guess for the full ERT-based reconstruction solution.To evaluate the performance of this hybrid method,we present extensive studies involving numerical tissue phantoms and experimental data.As a result,we show that the hybrid method reduces the reconstruction time by a factor of up to 23,depending on the physical character of the problem.
基金The Funding of Jiangsu Innovation Program for Graduate Educationgrant number:SJLX15_0115+1 种基金the Fundamental Research Funds for the Central Universities of Chinagrant number NZ2014101
文摘Bioluminescence imaging is a kind of emerging detection technology at cellular,molecular and genetic level.The most popular bioluminescence imaging model is diffusion approximation(DA).However,because of the ill-posedness of the DA-based inverse problem and the instability of reconstruction algorithms,the location accuracy of the reconstructed sources is low.Radiative transfer equation(RTE),which considers the direction of the photon migration and the effect of absorption and scattering in tissues,can accurately express the transmission of bioluminescent photons through the tissues.In this paper,we studied the bioluminescence imaging based on the RTE.2D simulations were performed,and quantitative evaluation was given by the absolute source position error,the relative source area error and the minimum bounding box.The results of the experiment showed that the imaging quality based on RTE was better than that one based on DA.
文摘Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational ax-isymmetric dusty gas, which has a variable azimuthal and axial fluid velocity. The dusty gas is assumed to be a mixture of small solid particles and perfect gas. The equi-librium flow conditions are assumed to be maintained, and the density of the mixture is assumed to be varying and obeying an exponential law. The fluid velocities in the ambient medium are assumed to obey exponential laws. The shock wave moves with variable velocity. The effects of variation of the mass concentration of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times. Also, a comparison between the solutions in the cases of isothermal and adia-batic flows is made.
基金National Numerical Windtunnel Project of China(NNW2018ZT2-A04,NNW2020ZT3-A22)National Natural Science Foundation of China(No.51906186).
文摘Prediction of the coupled conduction-radiation heat transfer in composite materials with periodic structure is important in high-temperature applications of the materials. The temperature dependence of thermal properties complicates the problem. In this work, a multiscale model is proposed for the conduction-radiation heat transfer in periodic composite materials with temperature-dependent thermal properties. Homogenization analysis of the coupled conduction and radiative transfer equations is conducted, in which the temperature dependence of thermal properties is considered. Both the macroscopic homogenized equations and the local unit cell problems are derived. It is proved that the macroscopic average temperature can be used in the unit cell problems for the first-order corrections of the temperature and radiative intensity, and the calculations of effective thermal properties. The temperature dependence of thermal properties only influences the higher-order corrections. A multiscale numerical method is proposed based on the analysis. The Gaussian process (GP) regression is coupled into the multiscale algorithm to build a correlation between thermal properties and temperature for the macroscale iterations and prevent the repetitive solving of unit cell problems. The GP model is updated by additional solutions of unit cell problems during the iteration according to a variance threshold. Numerical simulations of conduction-radiation heat transfer in composite with isotropic and anisotropic periodic structures are used to validate the proposed multiscale model. It is found that the accuracy and efficiency of the multiscale method can be guaranteed by using a proper variance threshold for the GP model. The multiscale model can provide both the average temperature and radiative intensity fields and their detailed fluctuations due to the local structures.
基金sponsored by the National Key R&D Program of China Grant No.2019YFA0709503(Z.X.)and No.2020YFA0712000(Z.M.)the Shanghai Sailing Program(Z.X.)+9 种基金the Natural Science Foundation of Shanghai Grant No.20ZR1429000(Z.X.)the National Natural Science Foundation of China Grant No.62002221(Z.X.)the National Natural Science Foundation of China Grant No.12101401(T.L.)the National Natural Science Foundation of China Grant No.12101402(Y.Z.)Shanghai Municipal of Science and Technology Project Grant No.20JC1419500(Y.Z.)the Lingang Laboratory Grant No.LG-QS-202202-08(Y.Z.)the National Natural Science Foundation of China Grant No.12031013(Z.M.)Shanghai Municipal of Science and Technology Major Project No.2021SHZDZX0102the HPC of School of Mathematical Sciencesthe Student Innovation Center at Shanghai Jiao Tong University.
文摘In this paper,we propose a machine learning approach via model-operatordata network(MOD-Net)for solving PDEs.A MOD-Net is driven by a model to solve PDEs based on operator representationwith regularization fromdata.For linear PDEs,we use a DNN to parameterize the Green’s function and obtain the neural operator to approximate the solution according to the Green’s method.To train the DNN,the empirical risk consists of the mean squared loss with the least square formulation or the variational formulation of the governing equation and boundary conditions.For complicated problems,the empirical risk also includes a fewlabels,which are computed on coarse grid points with cheap computation cost and significantly improves the model accuracy.Intuitively,the labeled dataset works as a regularization in addition to the model constraints.The MOD-Net solves a family of PDEs rather than a specific one and is much more efficient than original neural operator because few expensive labels are required.We numerically show MOD-Net is very efficient in solving Poisson equation and one-dimensional radiative transfer equation.For nonlinear PDEs,the nonlinear MOD-Net can be similarly used as an ansatz for solving nonlinear PDEs,exemplified by solving several nonlinear PDE problems,such as the Burgers equation.
文摘The present work concerns the numerical approximation of the M_(1) model for radiative transfer.The main purpose is to introduce an accurate finite volume method according to the nonlinear system of conservation laws that governs this model.We propose to derive an HLLC method which preserves the stationary contact waves.To supplement this essential property,the method is proved to be robust and to preserve the physical admissible states.Next,a relevant asymptotic preserving correction is proposed in order to obtain a method which is able to deal with all the physical regimes.The relevance of the numerical procedure is exhibited thanks to numerical simulations of physical interest.