Cures for the shock instability: development of a shock-stable Roe scheme

[1]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .

[2]  I. Flügge-Lotz,et al.  The interaction of a shock wave with a laminar boundary layer , 1968 .

[3]  V. Schmitt,et al.  Pressure distributions on the ONERA M6 wing at transonic Mach numbers , 1979 .

[4]  Stanley Osher,et al.  Upwind schemes and boundary conditions with applications to Euler equations in general geometries , 1983 .

[5]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[6]  J. R. Moselle,et al.  Studies of aerothermal loads generated in regions of shock/shock interaction in hypersonic flow , 1991 .

[7]  S. Imlay,et al.  Blunt-body flow simulations , 1988 .

[8]  P. Roe,et al.  On Godunov-type methods near low densities , 1991 .

[9]  J. Quirk.  A Contribution to the Great Riemann Solver Debate , 1994 .

[10]  F. Menter.  Two-equation eddy-viscosity turbulence models for engineering applications , 1994 .

[11]  A. Jameson.  ANALYSIS AND DESIGN OF NUMERICAL SCHEMES FOR GAS DYNAMICS, 2: ARTIFICIAL DIFFUSION AND DISCRETE SHOCK STRUCTURE , 1994 .

[12]  Hong-Chia Lin,et al.  Dissipation additions to flux-difference splitting , 1991 .

[13]  Meng-Sing Liou,et al.  An Accurate and Robust Flux Splitting Scheme for Shock and Contact Discontinuities , 1997, SIAM J. Sci. Comput..

[14]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[15]  Richard Sanders,et al.  Regular ArticleMultidimensional Dissipation for Upwind Schemes: Stability and Applications to Gas Dynamics☆ , 1998 .

[16]  Kun Xu,et al.  Gas-kinetic schemes for unsteady compressible flow simulations , 1998 .

[17]  Richard Sanders,et al.  Multidimensional Dissipation for Upwind Schemes , 1998 .

[18]  Kyu Hong Kim,et al.  An improvement of AUSM schemes by introducing the pressure-based weight functions , 1998 .

[19]  Jean-Marc Moschetta,et al.  Shock wave instability and the carbuncle phenomenon: same intrinsic origin? , 2000, Journal of Fluid Mechanics.

[20]  Jean-Marc Moschetta,et al.  Robustness versus accuracy in shock-wave computations , 2000 .

[21]  Meng-Sing Liou,et al.  Mass Flux Schemes and Connection to Shock Instability , 2000 .

[22]  Oh-Hyun Rho,et al.  Methods for the accurate computations of hypersonic flows: I. AUSMPW + scheme , 2001 .

[23]  Domenic D'Ambrosio,et al.  Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon , 2001 .