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.
Highlights
Simulation of high-speed, compressible flows requires proper design of inviscid numerical flux functions to capture shock waves, contact discontinuities, and shear layers in a stable and accurate manner
The results demonstrate that the HLLCT scheme is able to remain stable for very strong shocks
The contact-preserving shock-stable HLLCM scheme proposed by Shen et al.[10] presents a unique opportunity to explore the viability of a different approach to curing the carbuncle problem
Summary
Simulation of high-speed, compressible flows requires proper design of inviscid numerical flux functions to capture shock waves, contact discontinuities, and shear layers in a stable and accurate manner. One of the simplest and most robust flux schemes is the Harten-Lax-van Leer (HLL) scheme[2] in which an incomplete two-wave solution structure is assumed This incompleteness introduces non-physical dissipation of density and tangential momenta which precludes exact capturing of contact discontinuities and shear waves, resulting in highly diffused material interfaces and shear layers. The work of Shen et al.[10] is unique and illuminating They designed a modified HLLC scheme called HLLCM (where ‘M’ refers to the modification) based on the Rankine-Hugoniot jump conditions which preserves contact waves but smears shear waves. Unlike the more common HLLC-HLL hybrids, the HLLC-HLLCM hybrid scheme uses a contact-preserving complementary scheme This presents a unique opportunity to explore a radically new idea: to deactivate dissipation across shear layers rather than injecting additional dissipation along shock fronts.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
