A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

摘要: Abstract We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier–Stokes equations including laminar and turbulent flow. consider a semi-explicit high-order velocity-correction method time integration as well nodal equal-order discretizations velocity pressure. The non-linear convective term is treated explicitly while linear system solved pressure Poisson equation viscous term. key feature our solver consistent penalty reducing local divergence error in order to overcome recently reported instabilities spatially under-resolved high-Reynolds-number flows small steps. This similar grad–div stabilization widely used continuous finite elements. further review compare several other techniques proposed literature stabilize such flow configurations. specifically designed large-scale computations through matrix-free solvers preconditioning strategies tensor-product elements, which have allowed us scale this code up 34.4 billion degrees freedom 147,456 CPU cores. validate demonstrate optimal convergence rates with vortex problem past cylinder show applicability direct numerical implicit large-eddy channel at R e τ = 180 590.