Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier–Stokes equations

Simulation of the Taylor–Green Vortex Using High-Order Flux Reconstruction Schemes

“…Gaussian quadrature rules are employed [6]. Nodal DG (nDG) methods, in contrast, represent the solution as nodal values at a set of interpolation points [7].…”

“…Nodal DG (nDG) methods, in contrast, represent the solution as nodal values at a set of interpolation points [7]. By relinquishing exact integration, nDG methods are computationally cheaper but tend to require additional stabilization [6,7]. The DG Spectral Element Method (DGSEM) represents the solution in classical form but performs integration cheaply using cheap quadrature formulae [8,9].…”

Comparison of discontinuous Galerkin time integration schemes for the solution of flow problems with deformable domains

“…Although able to produce stable and high-order accurate solutions on fully unstructured meshes, the DG method is associated with a large number of unknowns, which with increasing problem size can substantially increase the computational demands. For this reason, the choice of a time integration method is of crucial importance [9,10].…”

“…For unsteady 3D viscous flow simulations in non-deforming domains, an answer to this question can be found in [9], where the authors compared various Jacobian free implicit methods with selected explicit ones. On the basis of the presented results, the authors concluded that explicit schemes can achieve approximately the same computational performance as the implicit ones when the LTS technique is applied, as well.…”

“…By following up the work of Birken et al [9], we try to find an answer to the question above by solving unsteady flow problems in time-varying domains, where the numerical solution is also dependent on the mapping procedure between the fixed reference configuration and the real domain. To determine the impact of time integration on CPU time usage and numerical error, we consider two well-known explicit and implicit time integration schemes -the explicit three-step Runge-Kutta method, performance of which is improved by the local time-stepping method, and the implicit CrankNicolson method.…”