The flux difference splitting(FDS)combined with the characteristic-wise weighted essentially non-oscillatory(WENO)reconstruction in single-component flow simulations is quite attractive and preferred for its better no...The flux difference splitting(FDS)combined with the characteristic-wise weighted essentially non-oscillatory(WENO)reconstruction in single-component flow simulations is quite attractive and preferred for its better non-oscillatory feature near discontinuities.However,when compressible multi-component flows are simulated,the FDS with the characteristic-wise WENO reconstruction may cause spurious oscillations.In this work,we analyze the reason that the oscillations are generated.A new method,which can effectively suppress this kind of spurious oscillations in multi-component flows,is proposed by modifying the total energy in the process of the WENO reconstruction.For example,in the fifth-order WENO reconstruction,on the global stencil S^(5)=(j-2,j-1,・・・,j+2)used to reconstruct the left-side value U_(j)^(L)+1/2,the total energy values are first modified by using the reconstructed value of the specific heat ratio(i.e.,γ_(j)^(L)+1/2,which can be directly reconstructed from the transport equation of the mass fraction),and then the characteristic-wise WENO reconstruction process is implemented.Numerical examples including several one-,two and threedimensional multi-component flows confirm the effectiveness and robustness of the proposed method.展开更多
This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is...This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied.The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact scheme.The solution algorithm used is the Beam-Warming approximate factorization scheme.Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are presented.The computed results are found in good agreement with established analytical and numerical results.The third-order accuracy of the scheme is verified on uniform rectangular meshes.展开更多
基金supported by NSFC Nos.12172364,11872097 and 91852203.
文摘The flux difference splitting(FDS)combined with the characteristic-wise weighted essentially non-oscillatory(WENO)reconstruction in single-component flow simulations is quite attractive and preferred for its better non-oscillatory feature near discontinuities.However,when compressible multi-component flows are simulated,the FDS with the characteristic-wise WENO reconstruction may cause spurious oscillations.In this work,we analyze the reason that the oscillations are generated.A new method,which can effectively suppress this kind of spurious oscillations in multi-component flows,is proposed by modifying the total energy in the process of the WENO reconstruction.For example,in the fifth-order WENO reconstruction,on the global stencil S^(5)=(j-2,j-1,・・・,j+2)used to reconstruct the left-side value U_(j)^(L)+1/2,the total energy values are first modified by using the reconstructed value of the specific heat ratio(i.e.,γ_(j)^(L)+1/2,which can be directly reconstructed from the transport equation of the mass fraction),and then the characteristic-wise WENO reconstruction process is implemented.Numerical examples including several one-,two and threedimensional multi-component flows confirm the effectiveness and robustness of the proposed method.
基金This work was supported by Natural Science Foundation of China(G10476032,G10531080)state key program for developing basic sciences(2005CB321703).
文摘This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates.The artificial compressibility approach is used,which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied.The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting,and the viscous terms are approximated by a fourth-order central compact scheme.The solution algorithm used is the Beam-Warming approximate factorization scheme.Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow,the liddriven cavity flow,and the constricting channel flow with varying geometry are presented.The computed results are found in good agreement with established analytical and numerical results.The third-order accuracy of the scheme is verified on uniform rectangular meshes.
