Corpus ID: 232134988

Energy relaxation approximation for the compressible multicomponent flows in thermal nonequilibrium

@article{Marmignon2021EnergyRA,
  title={Energy relaxation approximation for the compressible multicomponent flows in thermal nonequilibrium},
  author={C. Marmignon and F. Naddei and F. Renac},
  journal={ArXiv},
  year={2021},
  volume={abs/2103.03731}
}
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the hyperbolic system in homogeneous form. We derive a general framework for the design of numerical schemes for this model from numerical schemes for the monocomponent compressible Euler equations for a polytropic gas. Under a very simple condition on the… Expand
1 Citations
Entropy stable, robust and high-order DGSEM for the compressible multicomponent Euler equations
  • F. Renac
  • Computer Science, Mathematics
  • J. Comput. Phys.
  • 2021
TLDR
This work derives conditions on the numerical parameters to guaranty a semi-discrete entropy inequality as well as positivity of the cell average of the partial densities and internal energy of the fully discrete DGSEM at any approximation order and derives a two-point numerical flux satisfying the Tadmor's entropy conservation condition. Expand

References

SHOWING 1-10 OF 54 REFERENCES
Entropy stable, robust and high-order DGSEM for the compressible multicomponent Euler equations
  • F. Renac
  • Computer Science, Mathematics
  • J. Comput. Phys.
  • 2021
TLDR
This work derives conditions on the numerical parameters to guaranty a semi-discrete entropy inequality as well as positivity of the cell average of the partial densities and internal energy of the fully discrete DGSEM at any approximation order and derives a two-point numerical flux satisfying the Tadmor's entropy conservation condition. Expand
Relaxation schemes for the multicomponent Euler system
We show that it is possible to construct a class of entropic schemes for the multicomponent Euler system describing a gas or fluid homogeneous mixture at thermodynamic equilibrium by applying aExpand
Hybrid Multifluid Algorithms
  • Smadar Karni
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 1996
TLDR
A new algorithm based on the compressible Euler equations for multicomponent fluids augmented by the pressure evolution equation is presented and a hybrid scheme which selects from the two pressure update procedures is presented. Expand
RELAXATION OF FLUID SYSTEMS
We propose a relaxation framework for general fluid models which can be understood as a natural extension of the Suliciu approach in the Euler setting. In particular, the relaxation system may beExpand
Entropy and Entropy Production in Thermal and Chemical Non-Equilibrium Flows
The expressions for the entropy and the production of entropy in the general case of a mixture of perfect gases in non-equilibrium chemical and internal modes, including different translationalExpand
Relaxation of Energy and Approximate Riemann Solvers for General Pressure Laws in Fluid Dynamics
We consider the Euler equations for a compressible inviscid fluid with a general pressure law $p(\rho,\varepsilon)$, where $\rho$ represents the density of the fluid and $\varepsilon$ its specificExpand
Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems
We study the entropy stability of difference approximations to nonlinear hyperbolic conservation laws, and related time-dependent problems governed by additional dissipative and dispersive forcingExpand
Computation of weakly ionized hypersonic flows in thermochemical nonequilibrium
A numerical method to compute a two-dimensional hypersonic flowfield that is weakly ionized and in thermochemical nonequilibrium has been developed. Such a flowfield is described by coupled partialExpand
NONEQUILIBRIUM FLOW COMPUTATIONS I . An Analysis of Numerical Formulations of Conservation Laws
Modern numerical techniques employing properties of flux Jacobian matrices are extended to general, nonequilibrium flows. Generalizations of the BeamWarming scheme, Steger-Warming and van LeerExpand
A minimum entropy principle in the gas dynamics equations
Let u(@?x, t) be a weak solution of the Euler equation, governing the inviscid polytropic gas dynamics; in addition, u(@?x, t) is assumed to respect the usual entropy conditions connected with theExpand
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