On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems
Year: 2023
Author: Alexander V. Rodionov
Communications in Computational Physics, Vol. 34 (2023), Iss. 3 : pp. 749–786
Abstract
The article opens a series of publications devoted to a systematic study of numerical errors behind the shock wave when using high-order Godunov-type schemes, including in combination with the artificial viscosity approach. The proposed paper describes the numerical methods used in the study, and identifies the main factors affecting the accuracy of the solution for the case of one-dimensional gas dynamic problems. The physical interpretation of the identified factors is given and their influence on the grid convergence is analyzed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2022-0243
Communications in Computational Physics, Vol. 34 (2023), Iss. 3 : pp. 749–786
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 38
Keywords: Shock-capturing methods Riemann problem WENO reconstruction Runge-Kutta method Hancock-Rodionov method artificial viscosity approach Shu-Osher test problem.