A well-defined Godunov-type scheme in a Navier-Stokes model with a friction term

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Résumé

In this paper, particular attention is paid to Godunov-type numerical scheme for solving partial differential equations. We numerically approximate the weak solutions of the Navier-Stokes problem in the compressible case in one dimension of space with a friction term. The solutions of this model exhibit various properties that must be maintained accurately through numerical methods. Indeed, the solutions may satisfy stable regimes, the scheme mush maintain positive density throughout the flow. By developing a suitable approximate Riemann solver, a finite volume method is formulated to preserve as well as possible (or even exactly) those steady states of particular physical interest. Numerical simulations illustrate the effectiveness of the suggested computational method.

Mots-clés

Navier-Stokes equations, steady states, Godunov-type scheme, entropy inequality, compressible equations