On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems (Communications in Computational Physics, 2023)
The article opens a series of publications devoted to a systematic studyof numerical errors behind the shock wave when using high-order Godunov-typeschemes, including in combination with the artificial viscosity approach. The proposed paper describes the numerical methods used in the study, and identifies themain factors affecting the accuracy of the solution for the case of one-dimensional gasdynamic problems. The physical interpretation of the identified factors is given andtheir influence on the grid convergence is analyzed.
Keywords: Shock-capturing methods; Riemann problem; WENO reconstruction; Runge-Kutta method; Hancock-Rodionov method; artificial viscosity approach; Shu-Osher test problem.