The importance of eliminating errors in grid-metric evaluation for highorder difference schemes has been widely recognized in recent years,and it is known from the proof by Vinokur and Yee(NASA TM 209598,2000)that whe...The importance of eliminating errors in grid-metric evaluation for highorder difference schemes has been widely recognized in recent years,and it is known from the proof by Vinokur and Yee(NASA TM 209598,2000)that when conservative derivations of grid metric are used by Thomas,Lombard and Neier(AIAA J.,1978,17(10)and J.Spacecraft and rocket,1990,27(2)),errors caused by metric evaluation could be eliminated by linear schemes when flux splitting is not considered.According to the above achievement,central schemes without the use of flux splitting could fulfill the requirement of error elimination.Difficulties will arise for upwind schemes to attain the objective when the splitting is considered.In this study,further investigations are made on three aspects:Firstly,an idea of central scheme decomposition is introduced,and the procedure to derive the central scheme is proposed to evaluate grid metrics only.Secondly,the analysis has been made on the requirement of flux splitting to acquire free-stream preservation,and a Lax-Friedrichs-type splitting scheme is proposed as an example.Discussions about current study with that by Nonomura et al.(Computers and Fluids,2015,107)have been made.Thirdly,for halfnode-or mixed-type schemes,interpolations should be used to derive variables at half nodes.The requirement to achieve metric identity on this situation is analyzed and an idea of directionally consistent interpolation is proposed,which is manifested to be indispensable to avoid violations of metric identity and to eliminate metric-caused errors thereafter.Two numerical problems are tested,i.e.,the free-stream and vortex preservation onwavy,largely randomized and triangular-like grids.Numerical results validate aforementioned theoretical outcomes.展开更多
In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial deriv...In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.展开更多
It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth ...It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.展开更多
High order accurate scheme is highly desirable for Slow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a...High order accurate scheme is highly desirable for Slow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a third-order, upwind biased, shock capturing scheme was proposed. Also, a new shock fitting method, called pseudo shock fitting method, was suggested, which in principle can be with any order of accuracy. Test cases for one dimensional flows show that the new method is very satisfactory.展开更多
The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence. The mathematical model of the problem and upwind splitting alternating direction method w...The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence. The mathematical model of the problem and upwind splitting alternating direction method were presented. Using this method, the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Provivce was finished. The numerical results turned out to be identical with the real measurements, so the prediction of the consequences of protection projectects is reasonable.展开更多
A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and...A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.展开更多
The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. T...The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.展开更多
In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the...In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.展开更多
A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the cha...A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.展开更多
In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order converge...In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter e , to the solution of problem (1.1). Numerical results are finally provided.展开更多
The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechan...The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics (English Edition), 2007, 28(7), 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.展开更多
We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into ...We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].展开更多
The simulation of hypersonic flows with fully unstructured(tetrahedral)grids has severe problems with respect to the prediction of stagnation region heating,due to the random face orientation without alignment to the ...The simulation of hypersonic flows with fully unstructured(tetrahedral)grids has severe problems with respect to the prediction of stagnation region heating,due to the random face orientation without alignment to the bow shock.To improve the accuracy of aero-heating predictions,three multi-dimensional approaches on unstructured grids are coupled in our Reynolds-averaged Navier-Stokes(RANS)solver,including multi-dimensional upwind flux reconstruction(MUP),multi-dimensional limiter(MLP-u2)and multi-dimensional gradient reconstruction(MLR).The coupled multi-dimensional RANS solver is validated by several typical verification and validation(V&V)cases,including hypersonic flows over a cylinder,a blunt biconic,and a double-ellipsoid,with commonly used prism/tetrahedral hybrid grids.Finally,the coupled multi-dimensional solver is applied to simulating the heat flux distribution over a 3D engineering configuration,i.e.a Hermes-like space shuttle model.The obtained numerical results are compared with experimental data.The predicted results demonstrate that the coupled multi-dimensional approach has a good prediction capability on aerodynamic heating over a wide range of complex engineering configurations.展开更多
Upwind algorithms are becoming progressively popular for river flood routing due to their capability of resolving trans-critical flow regimes. For consistency, these algorithms suggest natural upwind discretization of...Upwind algorithms are becoming progressively popular for river flood routing due to their capability of resolving trans-critical flow regimes. For consistency, these algorithms suggest natural upwind discretization of the source term, which may be essential for natural channels with irregular geometry. Yet applications of these upwind algorithms to natural river flows are rare, and in such applications the traditional and simpler pointwise, rather than upwind discretization of the source term is used. Within the framework of a first-order upwind algorithm, this paper presents a comparison of upwind and pointwise discretizations of the source term. Numerical simulations were carried out for a selected irregular channel comprising a pool-riffle sequence Jn the River Lune, England with observed data. It is Shown that the impact of pointwise discretization, compared to the upwind, is appreciable mainly in flow zones with the Froude number closer to or larger than unity. The discrepancy due to pointwise and upwind discretizations of the source term is negligible in flow depth and hence in water surface elevation, but well manifested in mean velocity and derived flow quantities. Also the occurrence of flow reversal and equalisation over the pool-riffle sequence in response to increasing discharges is demonstrated.展开更多
We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on: 1. the numerical observation that classical first order monotone upwind sche...We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on: 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.展开更多
A bounded high order upwind scheme is presented for the modified Burgers’equation by using the normalized-variable formulation in the finite volume framework.The characteristic line of the present scheme in the norma...A bounded high order upwind scheme is presented for the modified Burgers’equation by using the normalized-variable formulation in the finite volume framework.The characteristic line of the present scheme in the normalizedvariable diagram is designed on the Hermite polynomial interpolation.In order to suppress unphysical oscillations,the present scheme respects both the TVD(total variational diminishing)constraint and CBC(convection boundedness criterion)condition.Numerical results demonstrate the present scheme possesses good robustness and high resolution for the modified Burgers’equation.展开更多
This paper analyzes a population model with time-dependent advection and an autocatalytic-type growth.As opposed to a logistic growth where the rate of growth of the population decreases from the onset,an autocatalyti...This paper analyzes a population model with time-dependent advection and an autocatalytic-type growth.As opposed to a logistic growth where the rate of growth of the population decreases from the onset,an autocatalytic growth has a point of inflection where the rate of growth switches from an increasing trend to a decreasing trend.Employing the idea of Painleve property,we show that a variety of exact traveling wave solutions can be obtained for this model depending on the choice of the advection term.In particular,due to situations in resource distribution or environmental variations,if the advection is represented as a decaying function in time or an oscillating function in time,we are able to find exact solutions with interesting behavior.We also carry out a computational study of the model using an exponentially upwinded numerical scheme and illustrate the movement of the solutions and their characteristics pictorially.展开更多
In this paper,we develop and study numerical methods for the two-mode shallow water equations recently proposed in[S.STECHMANN,A.MAJDA,and B.KHOUIDER,Theor.Comput.Fluid Dynamics,22(2008),pp.407–432].Designing a relia...In this paper,we develop and study numerical methods for the two-mode shallow water equations recently proposed in[S.STECHMANN,A.MAJDA,and B.KHOUIDER,Theor.Comput.Fluid Dynamics,22(2008),pp.407–432].Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms.We present several numerical approaches—two operator splitting methods(based on either Roe-type upwind or central-upwind scheme),a central-upwind scheme and a path-conservative centralupwind scheme—and test their performance in a number of numerical experiments.The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method。展开更多
A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around...A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes(RANS) equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method" and ‘‘minimum distance scheme of donor elements method" are established in this work. To improve the computational efficiency, Message Passing Interface(MPI) parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage(FAS) multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.展开更多
In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations (FNBE) in order to simulate wave transformation phenomena, wave breaking, runup and nearshore ...In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations (FNBE) in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-f'mite difference scheme. A high-order upwind weighted essentially non-oscillatory (WENO) finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations (NSWE). On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento (Italy).展开更多
基金This work is sponsored by the National Science Foundation of China under the Grant Number 11272037 and 91541105is also partially supported by National Key Basic Research and Development 973 Program of China under Grant Number 2014CB744100.
文摘The importance of eliminating errors in grid-metric evaluation for highorder difference schemes has been widely recognized in recent years,and it is known from the proof by Vinokur and Yee(NASA TM 209598,2000)that when conservative derivations of grid metric are used by Thomas,Lombard and Neier(AIAA J.,1978,17(10)and J.Spacecraft and rocket,1990,27(2)),errors caused by metric evaluation could be eliminated by linear schemes when flux splitting is not considered.According to the above achievement,central schemes without the use of flux splitting could fulfill the requirement of error elimination.Difficulties will arise for upwind schemes to attain the objective when the splitting is considered.In this study,further investigations are made on three aspects:Firstly,an idea of central scheme decomposition is introduced,and the procedure to derive the central scheme is proposed to evaluate grid metrics only.Secondly,the analysis has been made on the requirement of flux splitting to acquire free-stream preservation,and a Lax-Friedrichs-type splitting scheme is proposed as an example.Discussions about current study with that by Nonomura et al.(Computers and Fluids,2015,107)have been made.Thirdly,for halfnode-or mixed-type schemes,interpolations should be used to derive variables at half nodes.The requirement to achieve metric identity on this situation is analyzed and an idea of directionally consistent interpolation is proposed,which is manifested to be indispensable to avoid violations of metric identity and to eliminate metric-caused errors thereafter.Two numerical problems are tested,i.e.,the free-stream and vortex preservation onwavy,largely randomized and triangular-like grids.Numerical results validate aforementioned theoretical outcomes.
文摘In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.
文摘It is a major challenge for the airframe-inlet design of modern combat aircrafts,as the flow and electromagnetic wave propagation in the inlet of stealth aircraft are very complex.In this study,an aerodynamic/stealth optimization design method for an S-duct inlet is proposed.The upwind scheme is introduced to the aerodynamic adjoint equation to resolve the shock wave and flow separation.The multilevel fast multipole algorithm(MLFMA)is utilized for the stealth adjoint equation.A dorsal S-duct inlet of flying wing layout is optimized to improve the aerodynamic and stealth characteristics.Both the aerodynamic and stealth characteristics of the inlet are effectively improved.Finally,the optimization results are analyzed,and it shows that the main contradiction between aerodynamic characteristics and stealth characteristics is the centerline and crosssectional area.The S-duct is smoothed,and the cross-sectional area is increased to improve the aerodynamic characteristics,while it is completely opposite for the stealth design.The radar cross section(RCS)is reduced by phase cancelation for low frequency conditions.The method is suitable for the aerodynamic/stealth design of the aircraft airframe-inlet system.
文摘High order accurate scheme is highly desirable for Slow computation with shocks. After analysis has been made for the reason of the generation of non-physical oscillations around the shock in numerical computations, a third-order, upwind biased, shock capturing scheme was proposed. Also, a new shock fitting method, called pseudo shock fitting method, was suggested, which in principle can be with any order of accuracy. Test cases for one dimensional flows show that the new method is very satisfactory.
文摘The simulation of this process and the effects of protection projects lays the foundation of its effective control and defence. The mathematical model of the problem and upwind splitting alternating direction method were presented. Using this method, the numerical simulation of seawater intrusion in Laizhou Bay Area of Shandong Provivce was finished. The numerical results turned out to be identical with the real measurements, so the prediction of the consequences of protection projectects is reasonable.
文摘A mixed algorithm of central and upwind difference scheme for the solution of steady/unsteady incompressible Navier-Stokes equations is presented. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The numerical flux of semi-discrete equations is computed by using the Roe approximation. Time accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The algebraic turbulence model of Baldwin-Lomax is ulsed in this work. As examples, the solutions of flow through two dimensional flat, airfoil, prolate spheroid and cerebral aneurysm are computed and the results are compared with experimental data. The results show that the coefficient of pressure and skin friction are agreement with experimental data, the largest discrepancy occur in the separation region where the lagebraic turbulence model of Baldwin-Lomax could not exactly predict the flow.
文摘The traditional differential quadrature method was improved by using theupwind difference scheme for the convective terms to solve the coupled two-dimensionalincompressible Navier-stokes equations and heat equation. The new method was compared with theconventional differential quadrature method in the aspects of convergence and accuracy. The resultsshow that the new method is more accurate, and has better convergence than the conventionaldifferential quadrature method for numerically computing the steady-state solution.
基金NKBRSF CG 1990 3 2 80 5 National Natural Science F oundation of China !( No.5 98760 0 2 )
文摘In order to prevent smearing the discontinuity, a modified term is added to the third order Upwind Compact Difference scheme to lower the dissipation error. Moreover, the dispersion error is controled to hold back the non physical oscillation by means of the group velocity control. The scheme is used to simulate the interactions of shock density stratified interface and the disturbed interface developing to vortex rollers. Numerical results are satisfactory.
基金Project supported by the National Natural Science Foundation of China (Nos.10321002 and 10672012)
文摘A new shock-capturing method is proposed which is based on upwind schemes and flux-vector splittings. Firstly, original upwind schemes are projected along characteristic directions. Secondly, the amplitudes of the characteristic decompositions are carefully controlled by limiters to prevent non-physical oscillations. Lastly, the schemes are converted into conservative forms, and the oscillation-free shock-capturing schemes are acquired. Two explicit upwind schemes (2nd-order and 3rd-order) and three compact upwind schemes (3rd-order, 5th-order and 7th-order) are modified by the method for hyperbolic systems and the modified schemes are checked on several one-dimensional and two-dimensional test cases. Some numerical solutions of the schemes are compared with those of a WENO scheme and a MP scheme as well as a compact-WENO scheme. The results show that the method with high order accuracy and high resolutions can capture shock waves smoothly.
文摘In this paper, we consider the upwind difference scheme for singular perturbation problem (1.1). On a special discretization mesh, it is proved that the solution of the upwind difference scheme is first order convergent, uniformly in the small parameter e , to the solution of problem (1.1). Numerical results are finally provided.
基金Supported by the National Natural Science Foundation of China (Nos.50876114 and 10602043)the Program for New Century Excellent Talents in University,and the Scientific Research Key Project Fund of Ministry of Education (No.106142)
文摘The explicit compact difference scheme, proposed in Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD by Lin et al., published in Applied Mathematics and Mechanics (English Edition), 2007, 28(7), 943-953, has the same performance as the conventional finite difference schemes. It is just another expression of the conventional finite difference schemes. The proposed expression does not have the advantages of a compact difference scheme. Nonetheless, we can more easily obtain and implement compared with the conventional expression in which the coefficients can only be obtained by solving equations, especially for higher accurate schemes.
基金supported in part by the Knowledge Innovation Project of the Chinese Academy of Sciences Nos. K5501312S1 and K5502212F1, and NSFC grant No. 10601062supported in part by NSF grant Nos. DMS-0305081 and DMS-0608720, NSFC grant No. 10228101 and NSAF grant No. 10676017
文摘We study the L^l-error estimates for the upwind scheme to the linear advection equations with a piecewise constant coefficients modeling linear waves crossing interfaces. Here the interface condition is immersed into the upwind scheme. We prove that, for initial data with a bounded variation, the numerical solution of the immersed interface upwind scheme converges in L^l-norm to the differential equation with the corresponding interface condition. We derive the one-halfth order L^l-error bounds with explicit coefficients following a technique used in [25]. We also use some inequalities on binomial coefficients proved in a consecutive paper [32].
基金the National Key Research&Development Program of China(2016YFB020071)the National Natural Science Foundation of China(Grants 11532016 and 11702315).
文摘The simulation of hypersonic flows with fully unstructured(tetrahedral)grids has severe problems with respect to the prediction of stagnation region heating,due to the random face orientation without alignment to the bow shock.To improve the accuracy of aero-heating predictions,three multi-dimensional approaches on unstructured grids are coupled in our Reynolds-averaged Navier-Stokes(RANS)solver,including multi-dimensional upwind flux reconstruction(MUP),multi-dimensional limiter(MLP-u2)and multi-dimensional gradient reconstruction(MLR).The coupled multi-dimensional RANS solver is validated by several typical verification and validation(V&V)cases,including hypersonic flows over a cylinder,a blunt biconic,and a double-ellipsoid,with commonly used prism/tetrahedral hybrid grids.Finally,the coupled multi-dimensional solver is applied to simulating the heat flux distribution over a 3D engineering configuration,i.e.a Hermes-like space shuttle model.The obtained numerical results are compared with experimental data.The predicted results demonstrate that the coupled multi-dimensional approach has a good prediction capability on aerodynamic heating over a wide range of complex engineering configurations.
基金Project supported by the Open Research Fund of the State Key Laboratory of Water Resources and Hydropower Engineering Science, and the National Natural Science Foundation of China (Grant No: 50459001).
文摘Upwind algorithms are becoming progressively popular for river flood routing due to their capability of resolving trans-critical flow regimes. For consistency, these algorithms suggest natural upwind discretization of the source term, which may be essential for natural channels with irregular geometry. Yet applications of these upwind algorithms to natural river flows are rare, and in such applications the traditional and simpler pointwise, rather than upwind discretization of the source term is used. Within the framework of a first-order upwind algorithm, this paper presents a comparison of upwind and pointwise discretizations of the source term. Numerical simulations were carried out for a selected irregular channel comprising a pool-riffle sequence Jn the River Lune, England with observed data. It is Shown that the impact of pointwise discretization, compared to the upwind, is appreciable mainly in flow zones with the Froude number closer to or larger than unity. The discrepancy due to pointwise and upwind discretizations of the source term is negligible in flow depth and hence in water surface elevation, but well manifested in mean velocity and derived flow quantities. Also the occurrence of flow reversal and equalisation over the pool-riffle sequence in response to increasing discharges is demonstrated.
基金partially supported by ONR Grant N00014-02-1-0090ARO MURI Grant W911NF-07-1-0185NSF Grant DMS0811254
文摘We present a compact upwind second order scheme for computing the viscosity solution of the Eikonal equation. This new scheme is based on: 1. the numerical observation that classical first order monotone upwind schemes for the Eikonal equation yield numerical upwind gradient which is also first order accurate up to singularities; 2. a remark that partial information on the second derivatives of the solution is known and given in the structure of the Eikonal equation and can be used to reduce the size of the stencil. We implement the second order scheme as a correction to the well known sweeping method but it should be applicable to any first order monotone upwind scheme. Care is needed to choose the appropriate stencils to avoid instabilities.
基金This work is supported by the National Natural Science Foundation of China(Grant No.11061021)Key Project of Chinese Ministry of Education(12024)+1 种基金the Scientific Research Projection of Higher Schools of Inner Mongolia(NJ10016,NJ10006,NJZZ12011)the National Natural Science Foundation of Inner Mongolia Province(2011BS0102).
文摘A bounded high order upwind scheme is presented for the modified Burgers’equation by using the normalized-variable formulation in the finite volume framework.The characteristic line of the present scheme in the normalizedvariable diagram is designed on the Hermite polynomial interpolation.In order to suppress unphysical oscillations,the present scheme respects both the TVD(total variational diminishing)constraint and CBC(convection boundedness criterion)condition.Numerical results demonstrate the present scheme possesses good robustness and high resolution for the modified Burgers’equation.
文摘This paper analyzes a population model with time-dependent advection and an autocatalytic-type growth.As opposed to a logistic growth where the rate of growth of the population decreases from the onset,an autocatalytic growth has a point of inflection where the rate of growth switches from an increasing trend to a decreasing trend.Employing the idea of Painleve property,we show that a variety of exact traveling wave solutions can be obtained for this model depending on the choice of the advection term.In particular,due to situations in resource distribution or environmental variations,if the advection is represented as a decaying function in time or an oscillating function in time,we are able to find exact solutions with interesting behavior.We also carry out a computational study of the model using an exponentially upwinded numerical scheme and illustrate the movement of the solutions and their characteristics pictorially.
基金Spanish Government and FEDER through the Research project MTM2012-38383-C02-01the Andalusian Government through the project P11-FQM8179.The work of A.Chertock was supported in part by the NSF Grant DMS-1216974 and the ONR Grant N00014-12-1-0832The work of A.Kurganov was supported in part by the NSF Grant DMS-1216957 and the ONR Grant N00014-12-1-0833。
文摘In this paper,we develop and study numerical methods for the two-mode shallow water equations recently proposed in[S.STECHMANN,A.MAJDA,and B.KHOUIDER,Theor.Comput.Fluid Dynamics,22(2008),pp.407–432].Designing a reliable numerical method for this system is a challenging task due to its conditional hyperbolicity and the presence of nonconservative terms.We present several numerical approaches—two operator splitting methods(based on either Roe-type upwind or central-upwind scheme),a central-upwind scheme and a path-conservative centralupwind scheme—and test their performance in a number of numerical experiments.The obtained results demonstrate that a careful numerical treatment of nonconservative terms is crucial for designing a robust and highly accurate numerical method。
基金co-supported by the National Natural Science Foundation of China (Nos. 11272150, 10872094 and 10602024)
文摘A robust unsteady rotor flowfield solver CLORNS code is established to predict the complex unsteady aerodynamic characteristics of rotor flowfield. In order to handle the difficult problem about grid generation around rotor with complex aerodynamic shape in this CFD code,a parameterized grid generated method is established, and the moving-embedded grids are constructed by several proposed universal methods. In this work, the unsteady Reynolds-Averaged Navier-Stokes(RANS) equations with Spalart-Allmaras are selected as the governing equations to predict the unsteady flowfield of helicopter rotor. The discretization of convective fluxes is accomplished by employing the second-order central difference scheme, third-order MUSCL-Roe scheme, and fifth-order WENO-Roe scheme. Aimed at simulating the unsteady aerodynamic characteristics of helicopter rotor, the dual-time scheme with implicit LU-SGS scheme is employed to accomplish the temporal discretization. In order to improve the computational efficiency of holecells and donor elements searching of the moving-embedded grid technology, the ‘‘disturbance diffraction method" and ‘‘minimum distance scheme of donor elements method" are established in this work. To improve the computational efficiency, Message Passing Interface(MPI) parallel method based on subdivision of grid, local preconditioning method and Full Approximation Storage(FAS) multi-grid method are combined in this code. By comparison of the numerical results simulated by CLORNS code with test data, it is illustrated that the present code could simulate the aerodynamic loads and aerodynamic noise characteristics of helicopter rotor accurately.
文摘In this paper we propose a new model based on a contravariant integral form of the fully non-linear Boussinesq equations (FNBE) in order to simulate wave transformation phenomena, wave breaking, runup and nearshore currents in computational domains representing the complex morphology of real coastal regions. The above-mentioned contravariant integral form, in which Christoffel symbols are absent, is characterized by the fact that the continuity equation does not include any dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-f'mite difference scheme. A high-order upwind weighted essentially non-oscillatory (WENO) finite volume scheme that involves an exact Riemann solver is implemented. The wave breaking is represented by discontinuities of the weak solution of the integral form of the non-linear shallow water equations (NSWE). On the basis of the shock-capturing high order WENO scheme a new procedure, for the computation of the structure of the solution of a Riemann problem associated with a wet/dry front, is proposed in order to simulate the run up hydrodynamics in swash zone. The capacity of the proposed model to correctly represent wave propagation, wave breaking, run up and wave induced currents is verified against test cases present in literature. The results obtained are compared with experimental measures, analytical solutions or alternative numerical solutions. The proposed model is applied to a real case regarding the simulation of wave fields and nearshore currents in the coastal region opposite San Mauro Cilento (Italy).