On Godunov-type methods near low densities
Journal of Computational Physics
Dissipation additions to flux-difference splitting
Journal of Computational Physics
An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities
SIAM Journal on Scientific Computing
Multidimensional dissipation for upwind schemes: stability and applications to gas dynamics
Journal of Computational Physics
Mass flux schemes and connection to shock instability
Journal of Computational Physics
Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon
Journal of Computational Physics
Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme
Journal of Computational Physics
Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid Riemann solvers
Journal of Computational Physics
Multi-dimensional limiting process for three-dimensional flow physics analyses
Journal of Computational Physics
Use of e-AIRS computing service on CFD education and research
CLADE '08 Proceedings of the 6th international workshop on Challenges of large applications in distributed environments
Improving shock irregularities based on the characteristics of the MHD equations
Journal of Computational Physics
Robust HLLC Riemann solver with weighted average flux scheme for strong shock
Journal of Computational Physics
Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids
Journal of Computational Physics
A new approach of a limiting process for multi-dimensional flows
Journal of Computational Physics
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This paper deals with the development of an improved Roe scheme that is free from the shock instability and still preserves the accuracy and efficiency of the original Roe's Flux Difference Splitting (FDS). Roe's FDS is known to possess good accuracy but to suffer from the shock instability, such as the carbuncle phenomenon. As the first step towards a shock-stable scheme, Roe's FDS is compared with the HLLE scheme to identify the source of the shock instability. Through a linear perturbation analysis on the odd-even decoupling problem, damping characteristic is examined and Mach number-based functions f and g are introduced to balance damping and feeding rates, which leads to a shock-stable Roe scheme. In order to satisfy the conservation of total enthalpy, which is crucial in predicting surface heat transfer rate in high-speed steady flows, an analysis of dissipation mechanism in the energy equation is carried out to find out the error source and to make the proposed scheme preserve total enthalpy. By modifying the maximum-minimum wave speed, I the problem of expansion shock and numerical instability in the expansion region is also remedied without sacrificing the exact capturing of contact discontinuity. Various numerical tests concerned with the shock instability are performed to validate the robustness of the proposed scheme. Then, viscous flow test cases ranging from transonic to hypersonic regime are calculated to demonstrate the accuracy, robustness, and other essential features of the proposed scheme.