A mixed local discontinuous Galerkin scheme for capturing shock-driven instabilities in compressible multicomponent flows

Salman Saud Alsaeed; Satyvir Singh; Salman Saud Alsaeed; Satyvir Singh

doi:10.3934/math.20251160

AIMS Mathematics

2025, Volume 10, Issue 11: 26389-26417. doi: 10.3934/math.20251160

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A mixed local discontinuous Galerkin scheme for capturing shock-driven instabilities in compressible multicomponent flows

Salman Saud Alsaeed ¹,
Satyvir Singh ^{2,3
,
,}

1.
Department of Mathematics, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia
2.
Institute for Applied and Computational Mathematics, RWTH Aachen University, Germany
3.
Department of Mathematics, Graphic Era Deemed to be University, Dehradun, Uttarakhand, India

Received: 18 August 2025 Revised: 22 October 2025 Accepted: 06 November 2025 Published: 14 November 2025
MSC : 76L05, 76M22, 76T10

This study proposes a mixed local discontinuous Galerkin (LDG) scheme for capturing shock-driven interfacial instabilities in compressible multicomponent flows. The proposed scheme is validated through canonical test cases, including sod shock tube, shock-driven light/heavy cylinders, and chevron-shaped, and shows excellent agreement with experimental and numerical benchmarks. It effectively captures key mechanisms including shock refraction, baroclinic vorticity generation, vortex roll‐up, and nonlinear interface evolution. A systematic parametric analysis is carried out for the single‐mode heavy fluid layer configuration to examine the impact of interface thickness on shock-driven instability development. The results reveal that thinner interfaces intensify baroclinic vorticity deposition and accelerate the transition to nonlinear stages, whereas thicker interfaces delay instability growth and mitigate small‐scale structure formation. Spatially-integrated measures of baroclinic vorticity and enstrophy further confirm that geometric confinement plays a pivotal role in regulating vortex evolution and interfacial mixing.
- shock-driven instability,
- multicomponent compressible flows,
- mixed local discontinuous Galerkin,
- shock wave,
- baroclinic vorticity
Citation: Salman Saud Alsaeed, Satyvir Singh. A mixed local discontinuous Galerkin scheme for capturing shock-driven instabilities in compressible multicomponent flows[J]. AIMS Mathematics, 2025, 10(11): 26389-26417. doi: 10.3934/math.20251160

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Abstract

This study proposes a mixed local discontinuous Galerkin (LDG) scheme for capturing shock-driven interfacial instabilities in compressible multicomponent flows. The proposed scheme is validated through canonical test cases, including sod shock tube, shock-driven light/heavy cylinders, and chevron-shaped, and shows excellent agreement with experimental and numerical benchmarks. It effectively captures key mechanisms including shock refraction, baroclinic vorticity generation, vortex roll‐up, and nonlinear interface evolution. A systematic parametric analysis is carried out for the single‐mode heavy fluid layer configuration to examine the impact of interface thickness on shock-driven instability development. The results reveal that thinner interfaces intensify baroclinic vorticity deposition and accelerate the transition to nonlinear stages, whereas thicker interfaces delay instability growth and mitigate small‐scale structure formation. Spatially-integrated measures of baroclinic vorticity and enstrophy further confirm that geometric confinement plays a pivotal role in regulating vortex evolution and interfacial mixing.

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