In this paper,a conservative fifth-order upwind compact scheme using centered stencil is introduced.This scheme uses asymmetric coefficients to achieve the upwind property since the stencil is symmetric.Theoretical an...In this paper,a conservative fifth-order upwind compact scheme using centered stencil is introduced.This scheme uses asymmetric coefficients to achieve the upwind property since the stencil is symmetric.Theoretical analysis shows that the proposed scheme is low-dissipative and has a relatively large stability range.To maintain the convergence rate of the whole spatial discretization,a proper non-periodic boundary scheme is also proposed.A detailed analysis shows that the spatial discretization implemented with the boundary scheme proposed by Pirozzoli[J.Comput.Phys.,178(2001),pp.81–117]is approximately fourth-order.Furthermore,a hybridmethodology,coupling the compact scheme with WENO scheme,is adopted for problems with discontinuities.Numerical results demonstrate the effectiveness of the proposed scheme.展开更多
基金supported by National Natural Science Foundation of China(91130030).The authors are grateful to Dr.Jie Wu for his help on the manuscript.
文摘In this paper,a conservative fifth-order upwind compact scheme using centered stencil is introduced.This scheme uses asymmetric coefficients to achieve the upwind property since the stencil is symmetric.Theoretical analysis shows that the proposed scheme is low-dissipative and has a relatively large stability range.To maintain the convergence rate of the whole spatial discretization,a proper non-periodic boundary scheme is also proposed.A detailed analysis shows that the spatial discretization implemented with the boundary scheme proposed by Pirozzoli[J.Comput.Phys.,178(2001),pp.81–117]is approximately fourth-order.Furthermore,a hybridmethodology,coupling the compact scheme with WENO scheme,is adopted for problems with discontinuities.Numerical results demonstrate the effectiveness of the proposed scheme.
