A Fourth-Order Entropy Condition Scheme For Systems Of Hyperbolic Conservation Laws
ENGINEERING APPLICATIONS OF COMPUTATIONAL FLUID MECHANICS(2021)
摘要
Based on 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.
更多查看译文
关键词
Solution formula method, entropy condition, fully-discrete fourth-order accuracy, conservation laws, Euler equations
AI 理解论文
溯源树
样例
![](https://originalfileserver.aminer.cn/sys/aminer/pubs/mrt_preview.jpeg)
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要