A fourth-order entropy condition scheme for systems of hyperbolic conservation laws

Engineering Applications of Computational Fluid Mechanics

Tong Zhou¹  Haitao Dong¹ 

[1] NLCFD, School of Aeronautic Science and Engineering, Beihang University, Beijing, People’s Republic of Chin;

关键词: Solution formula method;    entropy condition;    fully-discrete fourth-order accuracy;    conservation laws;    Euler equations;   

DOI  :  10.1080/19942060.2021.1955010

来源: Taylor & Francis

【 摘 要 】

the analysis of the entropy condition scheme formulation, the accuracy order comes from initial value interpolation and flux reconstruction. Following the limiters of the traditional second-order Total Variation Diminishing scheme, higher accuracy order and non-oscillatory nature are retained with a newly proposed smoothness threshold method. Then, the scheme using the solution formula method in Dong et al. [(2002). High-order discontinuities decomposition entropy condition schemes for Euler equations. CFD Journal, 10(4), 563–568] is generalized to fully-discrete fourth-order accuracy, which retains the advantages of former schemes, i.e. it is a fully-discrete, one-step scheme with no need to perform with a Runge–Kutta process in time; an entropy condition is satisfied with no need of an entropy fix with artificial numerical viscosity; and an exact solution is achieved for linear cases if CFL→1. Numerical experiments are given with a 1D scalar equation for a shock-tube problem, a blast-wave problem, and Shu–Osher problem, a 2D Riemann problem, a double Mach reflection problem and a transonic airfoil flow problem for NACA0012. All tests are compared with a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme. Numerical experiments and efficiency comparisons show that the efficiency of the new fourth-order scheme is superior to the fifth-order WENO scheme.

【 授权许可】

CC BY