A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Matematicheskii Sbornik, vol.89, issue.3, pp.271-306, 1959. ,
, Finite volume methods for hyperbolic problems, vol.31, 2002.
Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, Journal of computational physics, vol.40, issue.2, pp.263-293, 1981. ,
Flux-vector splitting for the euler equation, Upwind and High-Resolution Schemes, pp.80-89, 1997. ,
Approximate riemann solvers, parameter vectors, and difference schemes, Journal of computational physics, vol.43, issue.2, pp.357-372, 1981. ,
Upwind difference schemes for hyperbolic systems of conservation laws, Mathematics of computation, vol.38, issue.158, pp.339-374, 1982. ,
On upstream differencing and godunov-type schemes for hyperbolic conservation laws, SIAM review, vol.25, issue.1, pp.35-61, 1983. ,
On godunov-type methods for gas dynamics, SIAM Journal on Numerical Analysis, vol.25, issue.2, pp.294-318, 1988. ,
Calculation of interaction of non-steady shock waves with obstacles, NRC, Division of Mechanical Engineering, 1962. ,
Robust hllc riemann solver with weighted average flux scheme for strong shock, Journal of Computational Physics, vol.228, issue.20, pp.7634-7642, 2009. ,
Riemann solvers and numerical methods for fluid dynamics: a practical introduction, 2013. ,
On godunovtype methods near low densities, Journal of computational physics, vol.92, issue.2, pp.273-295, 1991. ,
A contribution to the great riemann solver debate, Upwind and High-Resolution Schemes, pp.550-569, 1997. ,
Cures for numerical shock instability in hllc solver, International journal for numerical methods in fluids, vol.65, issue.9, pp.1026-1038, 2011. ,
A hybrid numerical method to cure numerical shock instability, Commun. Comput. Phys, vol.8, pp.1264-1271, 2010. ,
Very simple, carbuncle-free, boundary-layer-resolving, rotated-hybrid riemann solvers, Journal of Computational Physics, vol.227, issue.4, pp.2560-2581, 2008. ,
A robust hllc-type riemann solver for strong shock, Journal of Computational Physics, vol.309, pp.185-206, 2016. ,
Robust hll-type riemann solver capable of resolving contact discontinuity, Computers & Fluids, vol.63, pp.148-164, 2012. ,
Artificial viscosity in godunov-type schemes to cure the carbuncle phenomenon, Journal of Computational Physics, vol.345, pp.308-329, 2017. ,
Affordable shock-stable item for godunov-type schemes against carbuncle phenomenon, Journal of Computational Physics, vol.373, pp.662-672, 2018. ,
A new robust carbuncle-free roe scheme for strong shock, Journal of Scientific Computing, vol.77, issue.2, pp.1250-1277, 2018. ,
General procedure for riemann solver to eliminate carbuncle and shock instability, AIAA Journal, vol.55, issue.6, pp.2002-2015, 2017. ,
A cure for numerical shock instability in hllc riemann solver using antidiffusion control, Computers & Fluids, vol.174, pp.144-166, 2018. ,
A simple cure for numerical shock instability in the hllc riemann solver, Journal of Computational Physics, vol.378, pp.477-496, 2019. ,
Effective technique to improve shock anomalies and heating prediction for hypersonic flows, AIAA Journal, pp.1475-1479, 2017. ,
Boundary variation diminishing (bvd) reconstruction: A new approach to improve godunov schemes, Journal of Computational Physics, vol.322, pp.309-325, 2016. ,
Revisit to the thinc scheme: a simple algebraic vof algorithm, Journal of Computational Physics, vol.230, issue.19, pp.7086-7092, 2011. ,
A simple algebraic interface capturing scheme using hyperbolic tangent function, International Journal for Numerical Methods in Fluids, vol.48, issue.9, pp.1023-1040, 2005. ,
Simplified second-order godunov-type methods, SIAM Journal on Scientific and Statistical Computing, vol.9, issue.3, pp.445-473, 1988. ,
Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics, Journal of Computational Physics, vol.231, issue.22, pp.7504-7517, 2012. ,
A new efficient formulation of the hllem riemann solver for general conservative and nonconservative hyperbolic systems, Journal of Computational Physics, vol.304, pp.275-319, 2016. ,
An improved approximate riemann solver for hypersonic bidimensional flows, Fourteenth International Conference on Numerical Methods in Fluid Dynamics, pp.251-258, 1995. ,
Numerical instabilities in upwind methods: analysis and cures for the "carbuncle" phenomenon, Journal of Computational Physics, vol.166, issue.2, pp.271-301, 2001. ,
Limiter-free discontinuity-capturing scheme for compressible gas dynamics with reactive fronts, Computers & Fluids, vol.171, pp.1-14, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01791898
High fidelity discontinuity-resolving reconstruction for compressible multiphase flows with moving interfaces, Journal of Computational Physics, vol.371, pp.945-966, 2018. ,
Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov's method, Journal of computational Physics, vol.32, issue.1, pp.101-136, 1979. ,
On the behaviour of upwind schemes in the low mach number limit, Computers & fluids, vol.28, issue.1, pp.63-86, 1999. ,
URL : https://hal.archives-ouvertes.fr/hal-01534938
On entropy generation and dissipation of kinetic energy in highresolution shock-capturing schemes, Journal of Computational Physics, vol.227, issue.10, pp.4853-4872, 2008. ,
On the dissipation mechanism of upwind-schemes in the low mach number regime: A comparison between roe and hll, Journal of Computational Physics, vol.229, issue.2, pp.221-232, 2010. ,
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, Journal of computational physics, vol.27, issue.1, pp.1-31, 1978. ,
URL : https://hal.archives-ouvertes.fr/hal-01635155
Efficient implementation of essentially nonoscillatory shock-capturing schemes, Journal of computational physics, vol.77, issue.2, pp.439-471, 1988. ,
Classification of the riemann problem for two-dimensional gas dynamics, SIAM journal on mathematical analysis, vol.24, issue.1, pp.76-88, 1993. ,
Solution of two-dimensional riemann problems for gas dynamics without riemann problem solvers, Numerical Methods for Partial Differential Equations: An International Journal, vol.18, issue.5, pp.584-608, 2002. ,
A posteriori subcell limiting of the discontinuous galerkin finite element method for hyperbolic conservation laws, Journal of Computational Physics, vol.278, pp.47-75, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01914588
High resolution multi-moment finite volume method for supersonic combustion on unstructured grids, Applied Mathematical Modelling, vol.66, pp.404-423, 2019. ,
New accurate and efficient method for stiff detonation capturing, AIAA Journal, vol.56, issue.10, pp.4024-4038, 2018. ,
Initiation structure of oblique detonation waves behind conical shocks, Physics of Fluids, vol.29, issue.8, p.86104, 2017. ,
DOI : 10.1063/1.4999482
Effects of activation energy on the instability of oblique detonation surfaces with a one-step chemistry model, Physics of Fluids, vol.30, issue.10, p.106110, 2018. ,
Similarity and dimensional methods in mechanics, 1993. ,
A direct ale multi-moment finite volume scheme for the compressible euler equations, Communications in Computational Physics, vol.24, pp.1300-1325, 2018. ,
A skewed kernel approach for the simulation of shocks using sph, International Journal for Numerical Methods in Engineering, vol.111, issue.4, pp.383-400, 2017. ,
The numerical simulation of twodimensional fluid flow with strong shocks, Journal of computational physics, vol.54, issue.1, pp.115-173, 1984. ,
Anti-diffusive flux corrections for high order finite difference weno schemes, Journal of Computational Physics, vol.205, issue.2, pp.458-485, 2005. ,
DOI : 10.1016/j.jcp.2004.11.014
A multimass correction for multicomponent fluid flow simulation using smoothed particle hydrodynamics, International Journal for Numerical Methods in Engineering, vol.113, issue.13, pp.1929-1949, 2018. ,