On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves

Kolotilov, V. A.1; Kurganov, A. A.2,3,4; Ostapenko, V. V.1; Khandeeva, N. A.1; Chu, S.2

2023-07-01

10.1134/S0965542523070060

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS   Impact Factor & Quartile

0965-5425

1555-6662

A comparative experimental accuracy study of three shock-capturing schemes (the second-order CABARET, third-order Rusanov, and fifth-order in space third-order in time A-WENO schemes) is carried out by numerically solving a Cauchy problem with smooth periodic initial data for the Euler equations of gas dynamics. In the studied example, the solution breaks down and shock waves emerge. It is shown that the CABARET and A-WENO schemes, which are constructed using nonlinear limiters as a stabilization mechanism, have approximately the same accuracy in the areas of shock wave influence, while the nonmonotone Rusanov scheme has significantly higher accuracy in these areas despite producing noticeable nonphysical oscillations in the immediate vicinities of shock waves. At the same time, the combined scheme obtained based on the Rusanov and CABARET schemes localizes shock wave fronts, which are captured in a non-oscillatory manner, and preserves higher accuracy in the areas of the shock influence.

gas dynamic equations shock waves high-order shock-capturing schemes

SCI

English

Others

RSF[22-11-00060] ; RFBR[21-51-53012] ; NSFC["12111530004","12171226"] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]

Mathematics ; Physics

Mathematics, Applied ; Physics, Mathematical

WOS:001074795400014

PLEIADES PUBLISHING INC

MATHEMATICS

Web of Science

1.Russian Acad Sci, Siberian Branch, Lavrentyev Inst Hydrodynam, Novosibirsk 630090, Russia
2.Southern Univ Sci & Technol, Dept Math, Shenzhen 518005, Peoples R China
3.Southern Univ Sci & Technol, Shenzhen Int Ctr Math, Shenzhen 518005, Peoples R China
4.Southern Univ Sci & Technol, Guangdong Prov Key Lab Computat Sci & Mat Design, Shenzhen 518005, Peoples R China

Kolotilov, V. A.,Kurganov, A. A.,Ostapenko, V. V.,et al. On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS,2023,63(7).

Kolotilov, V. A.,Kurganov, A. A.,Ostapenko, V. V.,Khandeeva, N. A.,&Chu, S..(2023).On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves.COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS,63(7).

Kolotilov, V. A.,et al."On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves".COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 63.7(2023).