Assessment of three WENO type schemes for nonlinear conservative flux functions

INCAS Bulletin

Alina BOGOI¹  Dragos ISVORANU²  Sterian DANAILA³ 

[1] Department of Aerospace Engineering, University Politehnica of Bucharest Splaiul Independenţei 313, 060042, Bucharest, Romania, [e-mail];Department of Aerospace Engineering, University Politehnica of Bucharest Splaiul Independenţei 313, 060042, Bucharest, Romania, [e-mail];Department of Aerospace Engineering, University Politehnica of Bucharest Splaiul Independenţei 313, 060042, Bucharest, Romania, [e-mail];

关键词: Conservative law;    Riemann problem;    WENO-type schemes;    Runge-Kutta schemes;   

DOI  :  10.13111/2066-8201.2018.10.1.18

来源: DOAJ

【 摘 要 】

This paper focuses on a new comparison of the behavior of three Weighted Essentially Non-Oscillatory (WENO) type numerical schemes for three different nonlinear fluxes, in the case of scalar conservation law. The analytical solution is provided for various boundary conditions. For the time integration we adopt the 4-6 stage Low-Dispersion Low-Dissipation Runge-Kutta method (LDDRK 4-6). The schemes were tested on piecewise constant function for non-periodical conditions. The assessment was performed because the specialized literature mainly presents cases favorable illustrating only to a particular method while our purpose is to objectively present the performance and capacity of each method to simulate simple cases like scalar conservation law problems. All the schemes accurately identify the position of the shock and converge to the proper weak solution for the non-linear fluxes and different initial conditions. The paper is a continuation of the efficiency and accuracy analysis of high order numerical schemes previously published by the authors [1,2].

【 授权许可】

Unknown