Verification of WENO for hyperbolic conservation laws

Nicholas Dicati Pereira da Silva¹; Rafael Brandão de Rezende Borges²; Carlos Henrique Marchi¹; Luciano Kiyoshi Araki¹

¹ Federal University of Paraná; ² Rio de Janeiro State University

doi:10.20906/CPS/CILAMCE2017-0922

Resumo

Verification is an important procedure to assess numerical schemes and its solutions. One of the most popular numerical scheme is the Weighted Essentially Nonoscillatory (WENO). This scheme is high-order accurate and presents high resolution. The purpose of this work is to assess numerical solutions of three hyperbolic equations, namely, the linear advection equation and one-dimensional and two-dimensional Euler system of equations. In order to solve these equations, the Finite Volume Method was employed with an explicit formulation, Lax-Friedrichs flux, two numerical shcemes, first-order and WENO, and Runge-Kutta method. We have presented an error and order analysis for both numerical schemes, in which the WENO scheme showed fifth-order accuracy in all problems, except with discontinuous solutions as expected. We also confirmed that the WENO scheme is less dissipative even with discontinuities and in coarse meshes.

Palavras-chave: Verification; Hyperbolic conservation laws; WENO