Séminaires en 2026

In the first part of this talk, we present a high-order pressure-based solver for the 3D compressible Navier–Stokes equations operating uniformly at all Mach numbers. The method uses a cell-centered split of fast and slow fluxes, treated implicitly and explicitly, and introduces semi-implicit discretizations of kinetic energy and enthalpy that avoid iterative solvers. The resulting scheme leads to an elliptic pressure equation suitable for ideal and general EOS, solved with a nested Newton method when needed. High-order accuracy is achieved through IMEX time stepping and a dimension-by-dimension CWENO reconstruction for explicit convective and viscous terms. The implicit part uses central schemes without added dissipation, yielding a CFL condition based only on fluid velocity, and ensuring asymptotic preservation in the low-Mach limit. The second part presents an implicit DG-based discretization of the viscous terms, producing a discrete Laplacian built from high-order corner gradients in 3D and yielding a symmetric, positive-definite system. The final part introduces a Structure-Preserving DG (SPDG) operator that enforces the discrete div–curl identity to machine precision on staggered Cartesian grids. We illustrate its performance through simulations of incompressible Navier–Stokes equations in vortex–stream formulation and validate the robustness of the overall approach on a broad set of inviscid and viscous benchmark problems across all Mach regimes.

TBA