Higher-Order Discontinuous Galerkin Solvers for Incompressible Navier-Stokes Equations

Energy-Conserving Spectral Spatial Discretization on Unstructured Tetrahedral Meshes

Numerical simulations of high Reynolds number turbulent flows demand spatial discretizations that strictly conserve kinetic energy while preserving divergence-free velocity fields. We formulate an energy-stable, high-order Discontinuous Galerkin (DG) method equipped with interior penalty formulations and symmetric flux splitting. Simulations on canonical Taylor-Green vortex benchmarks demonstrate optimal spatial convergence up to polynomial degree p=7 without non-physical numerical dissipation. The proposed framework provides an exceptionally stable computational foundation for direct numerical simulation of complex turbulent boundary layers.