2019/07/08 by Charlotte Perrin, Perrin, Charlotte, Khaled Saleh +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1907.03610
openalex publication_date 2019/07/08 · openalex created_date 2019/07/12 · openalex updated_date 2026/07/28
In this paper, we propose a discretization of the multi-dimensional stationary compressible Navier-Stokes equations combining finite element and finite volume techniques. As the mesh size tends to 0, the numerical solutions are shown to converge (up to a subsequence) towards a weak solution of the continuous problem for ideal gas pressure laws p(ρ) = aρ γ , with γ > 3/2 in the three-dimensional case. It is the first convergence result for a numerical method with adiabatic exponents γ less than 3 when the space dimension is three. The present convergence result can be seen as a discrete counterpart of the construction of weak solutions established by P.-L. Lions and by S. Novo, A. Novotný.