On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems

Authors

  • Alexander V. Rodionov

DOI:

https://doi.org/10.4208/cicp.OA-2022-0243

Keywords:

Shock-capturing methods, Riemann problem, WENO reconstruction, Runge-Kutta method, Hancock-Rodionov method, artificial viscosity approach, Shu-Osher test problem.

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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Published

2023-10-07

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Issue

Vol. 34 No. 3 (2023)

Section

Articles

How to Cite

On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems. (2023). Communications in Computational Physics, 34(3), 749-786. https://doi.org/10.4208/cicp.OA-2022-0243