TY - JOUR
T1 - On the Solution Accuracy Downstream of Shocks When Using Godunov-Type Schemes. I. Sources of Errors in One-Dimensional Problems
AU - Rodionov , Alexander V.
JO - Communications in Computational Physics
VL - 3
SP - 749
EP - 786
PY - 2023
DA - 2023/10
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2022-0243
UR - https://global-sci.org/intro/article_detail/cicp/22023.html
KW - Shock-capturing methods, Riemann problem, WENO reconstruction, Runge-Kutta method, Hancock-Rodionov method, artificial viscosity approach, Shu-Osher test problem.
AB - <p style="text-align: justify;">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.</p>