High order residual distribution for steady state problems for hyperbolic conservation laws}

TL;DR

This paper introduces a high order residual distribution finite difference scheme using WENO-ZQ integration for steady state hyperbolic conservation laws, demonstrating high accuracy and shock resolution in various tests.

Contribution

The paper develops a novel high order residual distribution scheme with WENO-ZQ integration for steady state problems, enhancing accuracy and shock capturing capabilities.

Findings

Demonstrates high order accuracy in scalar and system problems

Shows effective shock resolution in numerical tests

Validates efficiency and robustness of the proposed method

Abstract

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods.