Several flux-splitting methods for the inviscid terms of the compressible-flow equations are derived for gases that are not in chemical equilibrium. Formulas are presented for the extension to chemical nonequilibrium of the Steger-Warming and Van Leer flux-vector splittings, and the Roe flux-difference splitting. The splittings are incorporated in a TVD algorithm and applied to one-dimensional ...

In the present work, the Roe, the Steger and Warming, the Van Leer, the Chakravarthy and Osher, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind structured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, the Chakravarth...

In the present work, the Roe, the Steger and Warming, the Van Leer, the Harten, the Frink, Parikh and Pirzadeh, the Liou and Steffen Jr. and the Radespiel and Kroll schemes are implemented, on a finite volume context and using an upwind and unstructured spatial discretization, to solve the Euler equations in the three-dimensional space. The Roe, the Harten, and the Frink, Parikh and Pirzadeh sc...

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe’s splitti...

Hypersonic flows around spatial vehicles during their reentry phase in planetary atmospheres are characterized by intense aerothermal phenomena. The aim of this work is to analyze high temperature flows around an axisymmetric blunt body taking into account chemical and vibrational non-equilibrium for air mixture species. For this purpose, a finite volume methodology is employed to determine the...

A parallel algorithm which has sufficient scalability for time accurate solution of a propagating detonation wavefront is developed. The emphasis is placed on reduction of computational time without compromising accuracy. The flow was assumed to be unsteady, inviscid and non-heat-conducting and coupled with finite-rate chemistry. A finite volume formulation was employed to ensure conservation a...

Fully implicit, fully coupled techniques are developed for simulating multiphase flow with nonequilibrium mass transfer between phases, with application to groundwater contaminant flow and transport. Numerical issues which are addressed include: use of MUSCL or Van Leer flux limiters to reduce numerical dispersion, use of full or approximate Jacobian for flux limiter methods, and variable subst...

Abstract—Hypersonic flows around spatial vehicles during their reentry phase in planetary atmospheres are characterized by intense aerothermodynamics phenomena. The aim of this work is to analyze high temperature flows around an axisymmetric blunt body taking into account chemical and vibrational non-equilibrium for air mixture species and the no slip condition at the wall. For this purpose, th...

The aim of this work is to analyze a viscous flow around the axisymmetric blunt body taken into account the mesh size both in the free stream and into the boundary layer. The resolution of the Navier-Stokes equations is realized by using the finite volume method to determine the flow parameters and detached shock position. The numerical technique uses the Flux Vector Splitting method of Van Lee...

We consider the nonlinear system of equations that results from the Van Leer flux vector-splitting discretization of the one dimensional Euler equations. This nonlinear system is linearized at the discrete solution. The main topic of this paper is a convergence analysis of blockGauss–Seidel methods applied to this linear system of equations. Both the lexicographic and the symmetric block-Gauss–...