Two-step weighting method for constructing fourth-order hybrid central WENO scheme

Liu, Shengping; Shen, Yiqing; Peng, Jun; Zhang, Jun

doi:10.1016/j.compfluid.2020.104590

Cited by 6 publications

(1 citation statement)

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“…Also, a Hermite WENO reconstruction method for the aforementioned temporal discretization framework was developed by Du and Li (2018). In the latest research, a kind of multistep WENO method (Peng & Shen, 2015;Shen et al, 2014) has been put forward whose accuracy near discontinuities is successfully improved, and they also proposed a two-step weighting method (Liu & Shen, 2020) that can easily be implemented for higher-order hybrid central WENO schemes. Using this method, they proposed a fourth-order hybrid central WENO scheme whose efficiency was increased in one test.…”

Section: Introductionmentioning

confidence: 99%

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

Zhou

Dong

2021

Engineering Applications of Computational Fluid Mechanics

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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 secondorder 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.

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