A space–time discontinuous Galerkin finite element method for the compressible Navier–Stokes equations is presented. We explain the space–time setting, derive the weak formulation and discuss our choices for the numerical fluxes. The resulting numerical method allows local grid adaptation as well as moving and deforming boundaries, which we illustrate by computing the flow around a 3D delta wing on an adapted mesh and by simulating the dynamic stall phenomenon of a 2D airfoil in rapid pitch-up maneuver.
- Discontinuous Galerkin finite element methods
- Arbitrary Lagrangian Eularian (ALE) formulation
- Compressible Navier–Stokes equations
- Numerical fluxes
Klaij, C. M., van der Vegt, J. J. W., & van der Ven, H. (2006). Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations. Journal of computational physics, 217(500-266/2), 589-611. [10.1016/j.jcp.2006.01.018]. https://doi.org/10.1016/j.jcp.2006.01.018