A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

doi:10.1007/s10483-021-2762-6

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (9): 1259-1278.doi: https://doi.org/10.1007/s10483-021-2762-6

A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

U. S. VEVEK¹, B. ZANG², T. H. NEW³

1. Department of Mechanical, Materials and Aerospace Engineering, University of Liverpool, Liverpool L69 3BX, United Kingdom;
2. Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, United Kingdom;
3. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

收稿日期:2021-03-20 修回日期:2021-06-07 发布日期:2021-09-07
通讯作者: T. H. NEW, E-mail:dthnew@ntu.edu.sg
基金资助:
the Singapore Ministry of Education AcRF Tier-2 Grant (No. MOE2014-T2-1-002) and the Graduate Research Officer Scholarship from School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

U. S. VEVEK¹, B. ZANG², T. H. NEW³

1. Department of Mechanical, Materials and Aerospace Engineering, University of Liverpool, Liverpool L69 3BX, United Kingdom;
2. Department of Aerospace Engineering, University of Bristol, Bristol BS8 1TR, United Kingdom;
3. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Received:2021-03-20 Revised:2021-06-07 Published:2021-09-07
Contact: T. H. NEW, E-mail:dthnew@ntu.edu.sg
Supported by:
the Singapore Ministry of Education AcRF Tier-2 Grant (No. MOE2014-T2-1-002) and the Graduate Research Officer Scholarship from School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

摘要/Abstract

摘要： A hybrid numerical flux scheme is proposed by adapting the carbuncle-free modified Harten-Lax-van Leer contact (HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact (HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.

关键词: carbuncle, shock instability, Euler equation, numerical flux, Harten-Lax-van Leer contact (HLLC) scheme

Abstract: A hybrid numerical flux scheme is proposed by adapting the carbuncle-free modified Harten-Lax-van Leer contact (HLLCM) scheme to smoothly revert to the Harten-Lax-van Leer contact (HLLC) scheme in regions of shear. This hybrid scheme, referred to as the HLLCT scheme, employs a novel, velocity-based shear sensor. In contrast to the non-local pressure-based shock sensors often used in carbuncle cures, the proposed shear sensor can be computed in a localized manner meaning that the HLLCT scheme can be easily introduced into existing codes without having to implement additional data structures. Through numerical experiments, it is shown that the HLLCT scheme is able to resolve shear layers accurately without succumbing to the shock instability.

Key words: carbuncle, shock instability, Euler equation, numerical flux, Harten-Lax-van Leer contact (HLLC) scheme

中图分类号:

U. S. VEVEK, B. ZANG, T. H. NEW. A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(9): 1259-1278.

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A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

A carbuncle cure for the Harten-Lax-van Leer contact (HLLC) scheme using a novel velocity-based sensor

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