Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme （m-UCD5） is proposed. The new difference scheme not only ret...Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme （m-UCD5） is proposed. The new difference scheme not only retains the advantage of good resolution of high wave number but also avoids the Gibbs phenomenon of the original upwind compact difference scheme. Compared with the classical 5th order WENO difference scheme, the new difference scheme is simpler and small in diffusion and computation load. By employing the component-wise and characteristic-wise methods, two forms of the new difference scheme are proposed to solve the N-S/Euler equation. Through the Sod problem, the Shu-Osher problem and tbe two-dimensional Double Mach Reflection problem, numerical solutions have demonstrated this new scheme does have a good resolution of high wave number and a robust ability of capturing shock waves, leading to a conclusion that the new difference scheme may be used to simulate complex flows containing shock waves.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 110632050, 10872205)the National Basic Research Program of China (Grant No. 2009CB724100)Projects of CAS INFO-115-B01
文摘Based on an upwind compact difference scheme and the idea of monotonicity-preserving, a 5th order monotonicity-preserving upwind compact difference scheme （m-UCD5） is proposed. The new difference scheme not only retains the advantage of good resolution of high wave number but also avoids the Gibbs phenomenon of the original upwind compact difference scheme. Compared with the classical 5th order WENO difference scheme, the new difference scheme is simpler and small in diffusion and computation load. By employing the component-wise and characteristic-wise methods, two forms of the new difference scheme are proposed to solve the N-S/Euler equation. Through the Sod problem, the Shu-Osher problem and tbe two-dimensional Double Mach Reflection problem, numerical solutions have demonstrated this new scheme does have a good resolution of high wave number and a robust ability of capturing shock waves, leading to a conclusion that the new difference scheme may be used to simulate complex flows containing shock waves.
