Dynamic light scattering(DLS)is a promising technique for early cataract detection and for studying cataractogenesis.A novel probabilistic analysis tool,the sparse Bayesian learning(SBL)algorithm,is described for reco...Dynamic light scattering(DLS)is a promising technique for early cataract detection and for studying cataractogenesis.A novel probabilistic analysis tool,the sparse Bayesian learning(SBL)algorithm,is described for reconstructing the most-probable size distribution ofα-crystallin and their aggregates in an ocular lens from the DLS data.The performance of the algorithm is evaluated by analyzing simulated correlation data from known distributions and DLS data from the ocular lenses of a fetal calf,a Rhesus monkey,and a man,so as to establish the required efficiency of the SBL algorithm for clinical studies.展开更多
In both fixed and rotary wing aircraft, the move toward lighter structures has resulted in an increase in structural vibration and interior noise. Porous materials have been proposed as acoustic absorbers to reduce th...In both fixed and rotary wing aircraft, the move toward lighter structures has resulted in an increase in structural vibration and interior noise. Porous materials have been proposed as acoustic absorbers to reduce this noise. This paper discusses the development of equipment at the NASA Glenn Research Center for characterizing the acoustic performance of porous materials: a flow resistance apparatus to measure the pressure drop across a specimen of porous material, and a standing wave tube that uses a pair of stationary microphones to measure the normal incidence acoustic impedance of a porous material specimen. Specific attention is paid to making this equipment as flexible as possible in terms of specimen sizes need for testing to accommodate the small or irregular sizes often produced during the development phase of a new material. In addition, due to the unknown performance of newly developed material, safety features are included on the flow resistance apparatus to contain test specimens that shed particles or catastrophically fail during testing. Results of measurements on aircraft fiberglass are presented to verify the correct performance of the equipment.展开更多
The phenol photocatalytic degradation was investigated using heterogeneous catalyst Ag-doped ZnO nanowires under UV irradiation. Ag-ZnO nanowires were immobilized on borosilicate glass via a simple hydrothermal techni...The phenol photocatalytic degradation was investigated using heterogeneous catalyst Ag-doped ZnO nanowires under UV irradiation. Ag-ZnO nanowires were immobilized on borosilicate glass via a simple hydrothermal technique. Preliminary photodegradation studies were performed with Ag-ZnO nanowires at various concentrations of phenol (10 - 60 mg/L) at undiluted pH. After determination of the optimal initial concentration (30 mg/L), additional parameters including pH and light intensity were investigated to optimize photodegradation of phenol for large-scale application. The experimental results illustrate that the kinetics of degradation of phenol are pseudo-first order. Based on the relationship, experimental model and empirical correlation were generated and compared for validity. The experimental data were found to fit a cubic model (linear in UV irradiation intensity, I, and cubic in pH), over ranges of 10 - 60 W (UV lamp power) and 2.7 - 11.0 (pH) with a coefficient of determination (R2) of 0.9934. This model, of the form K(I, pH) = c00 + c10I + c01pH + c11IpH + c02pH2 + c12IpH2 + c03pH3 was found to yield a better fit than simpler (quadratic) or more complex (quartic) polynomial-based models considered. The model parameters cij and corresponding 95% confidence intervals were obtained.展开更多
This study examined the improvement of microscopy segmentation intersection over union accuracy by transfer learning from a large dataset of microscopy images called MicroNet.Many neural network encoder architectures ...This study examined the improvement of microscopy segmentation intersection over union accuracy by transfer learning from a large dataset of microscopy images called MicroNet.Many neural network encoder architectures were trained on over 100,000 labeled microscopy images from 54 material classes.These pre-trained encoders were then embedded into multiple segmentation architectures including UNet and DeepLabV3+to evaluate segmentation performance on created benchmark microscopy datasets.Compared to ImageNet pre-training,models pre-trained on MicroNet generalized better to out-of-distribution micrographs taken under different imaging and sample conditions and were more accurate with less training data.When training with only a single Ni-superalloy image,pre-training on MicroNet produced a 72.2%reduction in relative intersection over union error.These results suggest that transfer learning from large in-domain datasets generate models with learned feature representations that are more useful for downstream tasks and will likely improve any microscopy image analysis technique that can leverage pre-trained encoders.展开更多
Damage mechanism identification has scientific and practical ramifications for the structural health monitoring,design,and application of composite systems.Recent advances in machine learning uncover pathways to ident...Damage mechanism identification has scientific and practical ramifications for the structural health monitoring,design,and application of composite systems.Recent advances in machine learning uncover pathways to identify the waveform-damage mechanism relationship in higher-dimensional spaces for a comprehensive understanding of damage evolution.This review evaluates the state of the field,beginning with a physics-based understanding of acoustic emission waveform feature extraction,followed by a detailed overview of waveform clustering,labeling,and error analysis strategies.Fundamental requirements for damage mechanism identification in any machine learning framework,including those currently in use,under development,and yet to be explored,are discussed.展开更多
In this work,we demonstrate that damage mechanism identification from acoustic emission(AE)signals generated in minicomposites with elastically similar constituents is possible.AE waveforms were generated by SiC/SiC c...In this work,we demonstrate that damage mechanism identification from acoustic emission(AE)signals generated in minicomposites with elastically similar constituents is possible.AE waveforms were generated by SiC/SiC ceramic matrix minicomposites(CMCs)loaded under uniaxial tension and recorded by four sensors(two models with each model placed at two ends).Signals were encoded with a modified partial power scheme and subsequently partitioned through spectral clustering.Matrix cracking and fiber failure were identified based on the frequency information contained in the AE event they produced,despite the similar constituent elastic properties of the matrix and fiber.Importantly,the resultant identification of AE events closely followed CMC damage chronology,wherein early matrix cracking is later followed by fiber breaks,even though the approach is fully domain-knowledge agnostic.Additionally,the partitions were highly precise across both the model and location of the sensors,and the partitioning was repeatable.The presented approach is promising for CMCs and other composite systems with elastically similar constituents.展开更多
Micro-thermal conductivity detector(μTCD)gas sensors work by detecting changes in the thermal conductivity of the surrounding medium and are used as detectors in many applications such as gas chromatography systems.C...Micro-thermal conductivity detector(μTCD)gas sensors work by detecting changes in the thermal conductivity of the surrounding medium and are used as detectors in many applications such as gas chromatography systems.Conventional TCDs use steady-state resistance(i.e.,temperature)measurements of a micro-heater.In this work,we developed a new measurement method and hardware configuration based on the processing of the transient response of a low thermal mass TCD to an electric current step.The method was implemented for a 100-μm-long and 1-μm-thick micro-fabricated bridge that consisted of doped polysilicon conductive film passivated with a 200-nm silicon nitride layer.Transient resistance variations of theμTCD in response to a square current pulse were studied in multiple mixtures of dilute gases in nitrogen.Simulations and experimental results are presented and compared for the time resolved and steady-state regime of the sensor response.Thermal analysis and simulation show that the sensor response is exponential in the transient state,that the time constant of this exponential variation was a linear function of the thermal conductivity of the gas ambient,and that the sensor was able to quantify the mixture composition.The level of detection in nitrogen was estimated to be from 25 ppm for helium to 178 ppm for carbon dioxide.With this novel approach,the sensor requires approximately 3.6 nJ for a single measurement and needs only 300μs of sampling time.This is less than the energy and time required for steady-state DC measurements.展开更多
An algorithm which allows the generation of representative volume elements(RVEs) for complex woven and warp-interlaced fiber-reinforced composite topologies while avoiding unphysical tow intersections is presented. Th...An algorithm which allows the generation of representative volume elements(RVEs) for complex woven and warp-interlaced fiber-reinforced composite topologies while avoiding unphysical tow intersections is presented. This is achieved by extending an existing RVE generation strategy in two significant ways:(1) the local cross section shape of the tow is adjusted depending on the local tow curvature in a way that preserves the cross sectional area of the tow, and(2) the elementary crimp interval is separated into a planar and a transition region. The modifications facilitate the generation of a wide range of elaborate textile topologies without tow intersections, which are present without the proposed modifications unless complex tow to tow contact models are introduced. The mechanical properties of plain weaves were predicted based on the topology generated with the proposed algorithm as well as based on RVEs which were constructed based on actual micrographs, i.e. a "digital twin" of the actual microstructure. A comparison of the predicted mechanical properties based on finite element and Multiscale Generalized Method of Cells techniques shows close agreement. However, some differences exist with respect to experimentally determined material parameters due to the finite dimensions of the specimens. Lastly,mechanical properties of multilayered weaves are predicted with the finite element method. The considered material systems are carbon fiber in epoxy matrix as well as C/C-SiC. However, the procedure is applicable to a wide range of material systems.展开更多
Three different multiscale models, based on the method of cells(generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the ...Three different multiscale models, based on the method of cells(generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the following multiscale modeling strategies were employed: Concurrent modeling of all phases using the generalized method of cells, synergistic(two-way coupling in space) multiscale modeling with the generalized method of cells, and hierarchical(one-way coupling in space) multiscale modeling with the high fidelity generalized method of cells. The three models are validated against data from a hierarchical multiscale finite element model in the literature for a repeating unit cell of C/C-SiC.Furthermore, the multiscale models are used in conjunction with classical lamination theory to predict the stiffness of C/C-SiC plates manufactured via a wet filament winding and liquid silicon infiltration process recently developed by the German Aerospace Institute. Finally, un-reacted Si(or free Si) and porosity in the C matrix are included in the multiscale model, and the effect of these new phases on the stiffness and local stresses are considered.展开更多
In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially ...In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially non-oscillatory(WENO-JS)scheme[8]and its variations[2,7],and the monotonicity preserving(MP)scheme[16],for solving the Euler equations.MP is found to be more effective than the three WENO variations studied.AUSM+-UP is also shown to be free of the so-called“carbuncle”phenomenon with the high-order interpolation.The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables,even though they require additional matrix-vector operations.Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison.In addition,four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy.Finally,a measure for quantifying the efficiency of obtaining high order solutions is proposed;the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.展开更多
A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via recons...A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via reconstruction).The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure.In addition to being simple and economical,it unifies several existing methods including discontinuous Galerkin,staggered grid,spectral volume,and spectral difference.To discretize the diffusion terms,we use the BR2(Bassi and Rebay),interior penalty,compact DG(CDG),and I-continuous approaches.The first three of these approaches,originally derived using the integral formulation,were recast here in the CPR framework,whereas the I-continuous scheme,originally derived for a quadrilateral mesh,was extended to a triangular mesh.Fourier stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried out.Finally,results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach.展开更多
Several recently developed AUSM-family numerical flux functions(SLAU,SLAU2,AUSM+-up2,and AUSMPW+)have been successfully extended to compute compressible multiphase flows,based on the stratified flow model concept,by f...Several recently developed AUSM-family numerical flux functions(SLAU,SLAU2,AUSM+-up2,and AUSMPW+)have been successfully extended to compute compressible multiphase flows,based on the stratified flow model concept,by following two previous works:one by M.-S.Liou,C.-H.Chang,L.Nguyen,and T.G.Theofanous[AIAA J.46:2345-2356,2008],in which AUSM+-up was used entirely,and the other by C.-H.Chang,and M.-S.Liou[J.Comput.Phys.225:840-873,2007],in which the exact Riemann solver was combined into AUSM+-up at the phase interface.Through an extensive survey by comparing flux functions,the following are found:(1)AUSM+-up with dissipation parameters of Kp and Ku equal to 0.5 or greater,AUSMPW+,SLAU2,AUSM+-up2,and SLAU can be used to solve benchmark problems,including a shock/water-droplet interaction;(2)SLAU shows oscillatory behaviors[though not as catastrophic as those of AUSM+(a special case of AUSM+-up with Kp=Ku=0)]due to insufficient dissipation arising from its ideal-gas-based dissipation term;and(3)when combined with the exact Riemann solver,AUSM+-up(Kp=Ku=1),SLAU2,and AUSMPW+are applicable to more challenging problems with high pressure ratios.展开更多
基金the National Science Council of the Republic of China under the Contract No.NSC-97-2112-M-006-006.
文摘Dynamic light scattering(DLS)is a promising technique for early cataract detection and for studying cataractogenesis.A novel probabilistic analysis tool,the sparse Bayesian learning(SBL)algorithm,is described for reconstructing the most-probable size distribution ofα-crystallin and their aggregates in an ocular lens from the DLS data.The performance of the algorithm is evaluated by analyzing simulated correlation data from known distributions and DLS data from the ocular lenses of a fetal calf,a Rhesus monkey,and a man,so as to establish the required efficiency of the SBL algorithm for clinical studies.
文摘In both fixed and rotary wing aircraft, the move toward lighter structures has resulted in an increase in structural vibration and interior noise. Porous materials have been proposed as acoustic absorbers to reduce this noise. This paper discusses the development of equipment at the NASA Glenn Research Center for characterizing the acoustic performance of porous materials: a flow resistance apparatus to measure the pressure drop across a specimen of porous material, and a standing wave tube that uses a pair of stationary microphones to measure the normal incidence acoustic impedance of a porous material specimen. Specific attention is paid to making this equipment as flexible as possible in terms of specimen sizes need for testing to accommodate the small or irregular sizes often produced during the development phase of a new material. In addition, due to the unknown performance of newly developed material, safety features are included on the flow resistance apparatus to contain test specimens that shed particles or catastrophically fail during testing. Results of measurements on aircraft fiberglass are presented to verify the correct performance of the equipment.
文摘The phenol photocatalytic degradation was investigated using heterogeneous catalyst Ag-doped ZnO nanowires under UV irradiation. Ag-ZnO nanowires were immobilized on borosilicate glass via a simple hydrothermal technique. Preliminary photodegradation studies were performed with Ag-ZnO nanowires at various concentrations of phenol (10 - 60 mg/L) at undiluted pH. After determination of the optimal initial concentration (30 mg/L), additional parameters including pH and light intensity were investigated to optimize photodegradation of phenol for large-scale application. The experimental results illustrate that the kinetics of degradation of phenol are pseudo-first order. Based on the relationship, experimental model and empirical correlation were generated and compared for validity. The experimental data were found to fit a cubic model (linear in UV irradiation intensity, I, and cubic in pH), over ranges of 10 - 60 W (UV lamp power) and 2.7 - 11.0 (pH) with a coefficient of determination (R2) of 0.9934. This model, of the form K(I, pH) = c00 + c10I + c01pH + c11IpH + c02pH2 + c12IpH2 + c03pH3 was found to yield a better fit than simpler (quadratic) or more complex (quartic) polynomial-based models considered. The model parameters cij and corresponding 95% confidence intervals were obtained.
基金This work was supported by the NASA Transformational Tools and Technologies(TTT)project under the Transformative Aeronautics Concept Program within the Aeronautics Research Mission Directorate.
文摘This study examined the improvement of microscopy segmentation intersection over union accuracy by transfer learning from a large dataset of microscopy images called MicroNet.Many neural network encoder architectures were trained on over 100,000 labeled microscopy images from 54 material classes.These pre-trained encoders were then embedded into multiple segmentation architectures including UNet and DeepLabV3+to evaluate segmentation performance on created benchmark microscopy datasets.Compared to ImageNet pre-training,models pre-trained on MicroNet generalized better to out-of-distribution micrographs taken under different imaging and sample conditions and were more accurate with less training data.When training with only a single Ni-superalloy image,pre-training on MicroNet produced a 72.2%reduction in relative intersection over union error.These results suggest that transfer learning from large in-domain datasets generate models with learned feature representations that are more useful for downstream tasks and will likely improve any microscopy image analysis technique that can leverage pre-trained encoders.
基金CM.and B.S.gratefully acknowledge financial support from the NASA Spce Tochnology Gaduate Research Opportunites Felowship(Grants:8ONSSC19K1164 and 8ONSSC17K0084,SD.and T.MP.gratefully acknowiedge fnanchl support from the Natonal Sclonce Found ation Uward 1984641)patt of the HDR IDEAS Insatute.The authors additonally thank Aaron Engel for the suggeston for this project and Dr Neal Brodnik for an Introduction to tSNE。
文摘Damage mechanism identification has scientific and practical ramifications for the structural health monitoring,design,and application of composite systems.Recent advances in machine learning uncover pathways to identify the waveform-damage mechanism relationship in higher-dimensional spaces for a comprehensive understanding of damage evolution.This review evaluates the state of the field,beginning with a physics-based understanding of acoustic emission waveform feature extraction,followed by a detailed overview of waveform clustering,labeling,and error analysis strategies.Fundamental requirements for damage mechanism identification in any machine learning framework,including those currently in use,under development,and yet to be explored,are discussed.
基金C.M.and B.S.gratefully acknowledge financial support from the NASA Space Technology Research Grant Program(Grants:80NSSC19K1164 and 80NSSC17K0084)S.D.and T.M.P.gratefully acknowledge financial support from the National Science Foundation(Award:1934641)as part of the HDR IDEAS2 Institute.The authors thank Abed Musaffar for creating the CAD schematic in Fig.1a and thank Dr.Neal Brodnik for a detailed introduction to t-SNE.
文摘In this work,we demonstrate that damage mechanism identification from acoustic emission(AE)signals generated in minicomposites with elastically similar constituents is possible.AE waveforms were generated by SiC/SiC ceramic matrix minicomposites(CMCs)loaded under uniaxial tension and recorded by four sensors(two models with each model placed at two ends).Signals were encoded with a modified partial power scheme and subsequently partitioned through spectral clustering.Matrix cracking and fiber failure were identified based on the frequency information contained in the AE event they produced,despite the similar constituent elastic properties of the matrix and fiber.Importantly,the resultant identification of AE events closely followed CMC damage chronology,wherein early matrix cracking is later followed by fiber breaks,even though the approach is fully domain-knowledge agnostic.Additionally,the partitions were highly precise across both the model and location of the sensors,and the partitioning was repeatable.The presented approach is promising for CMCs and other composite systems with elastically similar constituents.
基金The sensor that was tested in this work is based on the patents:No.7,911,010,No.8,426,932 and No.8,884,382.
文摘Micro-thermal conductivity detector(μTCD)gas sensors work by detecting changes in the thermal conductivity of the surrounding medium and are used as detectors in many applications such as gas chromatography systems.Conventional TCDs use steady-state resistance(i.e.,temperature)measurements of a micro-heater.In this work,we developed a new measurement method and hardware configuration based on the processing of the transient response of a low thermal mass TCD to an electric current step.The method was implemented for a 100-μm-long and 1-μm-thick micro-fabricated bridge that consisted of doped polysilicon conductive film passivated with a 200-nm silicon nitride layer.Transient resistance variations of theμTCD in response to a square current pulse were studied in multiple mixtures of dilute gases in nitrogen.Simulations and experimental results are presented and compared for the time resolved and steady-state regime of the sensor response.Thermal analysis and simulation show that the sensor response is exponential in the transient state,that the time constant of this exponential variation was a linear function of the thermal conductivity of the gas ambient,and that the sensor was able to quantify the mixture composition.The level of detection in nitrogen was estimated to be from 25 ppm for helium to 178 ppm for carbon dioxide.With this novel approach,the sensor requires approximately 3.6 nJ for a single measurement and needs only 300μs of sampling time.This is less than the energy and time required for steady-state DC measurements.
基金support from the Excellence Initiative of the German federal and state governments (GS018/OPBF051)funding through the von Kármán fellowship GS069+3 种基金the Alexander von Humboldt FoundationFunding by the Ministry of Innovation, Science and Research of the State of North Rhine-Westphalia is acknowledged by J.-W. Simonthe support from the Space Technology Mission Directorate Composite Technology for Exploration Projectthe Aeronautics Research Directorate Transformational Tools and Technologies Project
文摘An algorithm which allows the generation of representative volume elements(RVEs) for complex woven and warp-interlaced fiber-reinforced composite topologies while avoiding unphysical tow intersections is presented. This is achieved by extending an existing RVE generation strategy in two significant ways:(1) the local cross section shape of the tow is adjusted depending on the local tow curvature in a way that preserves the cross sectional area of the tow, and(2) the elementary crimp interval is separated into a planar and a transition region. The modifications facilitate the generation of a wide range of elaborate textile topologies without tow intersections, which are present without the proposed modifications unless complex tow to tow contact models are introduced. The mechanical properties of plain weaves were predicted based on the topology generated with the proposed algorithm as well as based on RVEs which were constructed based on actual micrographs, i.e. a "digital twin" of the actual microstructure. A comparison of the predicted mechanical properties based on finite element and Multiscale Generalized Method of Cells techniques shows close agreement. However, some differences exist with respect to experimentally determined material parameters due to the finite dimensions of the specimens. Lastly,mechanical properties of multilayered weaves are predicted with the finite element method. The considered material systems are carbon fiber in epoxy matrix as well as C/C-SiC. However, the procedure is applicable to a wide range of material systems.
基金NASA’s Transformational Tools and Technologies (TTT)the Theodore von Kármán Fellowship (GS069)+3 种基金the Theodore von Kármán Fellowship (GS069)the Alexander von Humboldt Fellowship for funding this workthe support of the Ministry of Innovation, Science, and Research of the state of North RhineWestphaliaprovided by the German Research Foundation (DFG) in the framework of CRC/Transregio 40 ‘Fundamental Technologies for the Development of Future Space-Transport-System Components under High Thermal and Mechanical Loads’ (TPD3)
文摘Three different multiscale models, based on the method of cells(generalized and high fidelity) micromechanics models were developed and used to predict the elastic properties of C/C-SiC composites. In particular, the following multiscale modeling strategies were employed: Concurrent modeling of all phases using the generalized method of cells, synergistic(two-way coupling in space) multiscale modeling with the generalized method of cells, and hierarchical(one-way coupling in space) multiscale modeling with the high fidelity generalized method of cells. The three models are validated against data from a hierarchical multiscale finite element model in the literature for a repeating unit cell of C/C-SiC.Furthermore, the multiscale models are used in conjunction with classical lamination theory to predict the stiffness of C/C-SiC plates manufactured via a wet filament winding and liquid silicon infiltration process recently developed by the German Aerospace Institute. Finally, un-reacted Si(or free Si) and porosity in the C matrix are included in the multiscale model, and the effect of these new phases on the stiffness and local stresses are considered.
基金supported by the Subsonic Fixed Wing and Supersonics Projects under the NASA’s Fundamental Aeronautics Program,Aeronautics Mission Directorate.We also thank H.T.Huynh of NASA Glenn Research Center for his help with the MP method。
文摘In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially non-oscillatory(WENO-JS)scheme[8]and its variations[2,7],and the monotonicity preserving(MP)scheme[16],for solving the Euler equations.MP is found to be more effective than the three WENO variations studied.AUSM+-UP is also shown to be free of the so-called“carbuncle”phenomenon with the high-order interpolation.The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables,even though they require additional matrix-vector operations.Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison.In addition,four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy.Finally,a measure for quantifying the efficiency of obtaining high order solutions is proposed;the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.
文摘A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by Wang and Gao is renamed CPR(correction procedure or collocation penalty via reconstruction).The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure.In addition to being simple and economical,it unifies several existing methods including discontinuous Galerkin,staggered grid,spectral volume,and spectral difference.To discretize the diffusion terms,we use the BR2(Bassi and Rebay),interior penalty,compact DG(CDG),and I-continuous approaches.The first three of these approaches,originally derived using the integral formulation,were recast here in the CPR framework,whereas the I-continuous scheme,originally derived for a quadrilateral mesh,was extended to a triangular mesh.Fourier stability and accuracy analyses for these schemes on quadrilateral and triangular meshes are carried out.Finally,results for the Navier-Stokes equations are shown to compare the various schemes as well as to demonstrate the capability of the CPR approach.
文摘Several recently developed AUSM-family numerical flux functions(SLAU,SLAU2,AUSM+-up2,and AUSMPW+)have been successfully extended to compute compressible multiphase flows,based on the stratified flow model concept,by following two previous works:one by M.-S.Liou,C.-H.Chang,L.Nguyen,and T.G.Theofanous[AIAA J.46:2345-2356,2008],in which AUSM+-up was used entirely,and the other by C.-H.Chang,and M.-S.Liou[J.Comput.Phys.225:840-873,2007],in which the exact Riemann solver was combined into AUSM+-up at the phase interface.Through an extensive survey by comparing flux functions,the following are found:(1)AUSM+-up with dissipation parameters of Kp and Ku equal to 0.5 or greater,AUSMPW+,SLAU2,AUSM+-up2,and SLAU can be used to solve benchmark problems,including a shock/water-droplet interaction;(2)SLAU shows oscillatory behaviors[though not as catastrophic as those of AUSM+(a special case of AUSM+-up with Kp=Ku=0)]due to insufficient dissipation arising from its ideal-gas-based dissipation term;and(3)when combined with the exact Riemann solver,AUSM+-up(Kp=Ku=1),SLAU2,and AUSMPW+are applicable to more challenging problems with high pressure ratios.