论文信息 - On TVD difference schemes for the three-dimensional Euler equations in general co-ordinates

On TVD difference schemes for the three-dimensional Euler equations in general co-ordinates

An improved treatment for the Harten–Yee and Chakravarthy–Osher TVD numerical flux functions in general co-ordinates is presented. The proposed formulation is demonstrated by a series of numerical experiments for three-dimensional flows around the ONERA-M6 wing. The numerical results indicate that it is important to use a suitable artificial compression parameter in order to obtain more accurate solutions around the leading edge of the wing. The two TVD numerical fluxes give excellent results: they capture the shock wave without numerical oscillations, they capture the rapid expansion around the leading edge sharply, they have self-adjusting mechanisms regarding numerical viscosity and they also have robustness.

[1] R. F. Warming,et al. An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. [application to Eulerian gasdynamic equations , 1976 .

[2] V. Schmitt,et al. Pressure distributions on the ONERA M6 wing at transonic Mach numbers , 1979 .

[3] S. Osher,et al. Uniformly High-Order Accurate Nonoscillatory Schemes. I , 1987 .

[4] H. C. Yee,et al. Numerical simulation of shock wave diffraction by TVD schemes , 1987 .

[5] T. Pulliam,et al. A diagonal form of an implicit approximate-factorization algorithm , 1981 .

[6] J. Steger,et al. Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms. [computational fluid dynamics , 1985 .

[7] H. C. Yee,et al. Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations. [in gas dynamics , 1985 .

[8] S. Osher,et al. A new class of high accuracy TVD schemes for hyperbolic conservation laws. [Total Variation Diminishing] , 1985 .

[9] H. C. Yee,et al. Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates , 1987 .