A low diffusion flux-split scheme for all Mach number flows

A Gogoi, JC Mandal - Physics of Fluids, 2023 - pubs.aip.org
A low diffusion version of the Harten–Lax–Leer convective pressure split (HLL-CPS) scheme
for resolving the shear layers and the flow features at low Mach numbers is presented here …

Development of a carbuncle-free and low-dissipation Roe-type scheme: Applications to multidimensional Euler flows

L Hu, Z Feng - Communications in Nonlinear Science and Numerical …, 2023 - Elsevier
The Roe scheme is known to have high resolution but to be afflicted by the notorious shock
anomalies (such as the carbuncle phenomena) and the unphysical expansion shocks. This …

A shock-stable numerical scheme accurate for contact discontinuities: Applications to 3D compressible flows

L Hu, X Wang - Communications in Nonlinear Science and Numerical …, 2024 - Elsevier
The low-dissipation Roe scheme is a popular shock capturing scheme but the shock
instability, such as the infamous carbuncle phenomenon, seriously affects its application in …

Numerical stability analysis of shock-capturing methods for strong shocks I: second-order MUSCL schemes

W Ren, W Xie, Y Zhang, H Yu, Z Tian - arXiv preprint arXiv:2305.03281, 2023 - arxiv.org
Modern shock-capturing schemes often suffer from numerical shock anomalies if the flow
field contains strong shocks, which may limit their further application in hypersonic flow …

Robust and accurate Roe-type Riemann solver with compact stencil: Rotated-RoeM scheme

S Choi, D Kim, J Park, JS Park - Journal of Computational Physics, 2024 - Elsevier
In this study, we aim to develop a robust and accurate Riemann solver to resolve strong
shock waves with compact stencil information by applying the rotated hybrid concept to the …

Numerical stability analysis of Godunov-type schemes for high Mach number flow simulations

W Ren, W Xie, Y Zhang, H Yu, Z Tian, J Zhu - Physics of Fluids, 2024 - pubs.aip.org
Modern shock-capturing schemes often suffer from numerical shock instabilities when
simulating strong shocks, limiting their application in supersonic or hypersonic flow …

Stability evaluation of approximate Riemann solvers using the direct Lyapunov method

A Gogoi, JC Mandal, A Saraf - Journal of Computational Physics, 2025 - Elsevier
The paper presents a new approach of stability evaluation of the approximate Riemann
solvers based on the direct Lyapunov method. The present methodology offers a detailed …

Further studies on numerical instabilities of Godunov-type schemes for strong shocks

W Xie, Z Tian, Y Zhang, H Yu, W Ren - Computers & Mathematics with …, 2021 - Elsevier
In this paper, continuous research is undertaken to explore the underlying mechanism of
numerical shock instabilities of Godunov-type schemes for strong shocks. By conducting …

A unified construction of all-speed HLL-type schemes for hypersonic heating computations

W Xie, Z Tian, Y Zhang, H Yu, W Ren - Computers & Fluids, 2022 - Elsevier
In this paper, a unified framework to develop all-speed HLL-type schemes for hypersonic
heating computations is constructed. Such a unified construction method combines two …

Enhanced HLLEM and HLL-CPS schemes for all Mach number flows based using anti-diffusion coefficients

A Gogoi, JC Mandal - arXiv preprint arXiv:2411.09509, 2024 - arxiv.org
This paper compares the HLLEM and HLL-CPS schemes for Euler equations and proposes
improvements for all Mach number flows. Enhancements to the HLLEM scheme involve …