A class of large time step Godunov schemes for hyperbolic conservation laws and applications |
| |
Authors: | ZhanSen Qian Chun-Hian Lee |
| |
Institution: | National Lab. for Computational Fluid Dynamics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China |
| |
Abstract: | A large time step (LTS) Godunov scheme firstly proposed by LeVeque is further developed in the present work and applied to Euler equations. Based on the analysis of the computational performances of LeVeque’s linear approximation on wave interactions, a multi-wave approximation on rarefaction fan is proposed to avoid the occurrences of rarefaction shocks in computations. The developed LTS scheme is validated using 1-D test cases, manifesting high resolution for discontinuities and the capability of maintaining computational stability when large CFL numbers are imposed. The scheme is then extended to multidimensional problems using dimensional splitting technique; the treatment of boundary condition for this multidimensional LTS scheme is also proposed. As for demonstration problems, inviscid flows over NACA0012 airfoil and ONERA M6 wing with given swept angle are simulated using the developed LTS scheme. The numerical results reveal the high resolution nature of the scheme, where the shock can be captured within 1–2 grid points. The resolution of the scheme would improve gradually along with the increasing of CFL number under an upper bound where the solution becomes severely oscillating across the shock. Computational efficiency comparisons show that the developed scheme is capable of reducing the computational time effectively with increasing the time step (CFL number). |
| |
Keywords: | Large time step Efficient computation Hyperbolic conservation laws Interactions of waves Rarefaction wave |
本文献已被 ScienceDirect 等数据库收录! |