We present a communicationand data-sensitive formulation of ADER-DG for hyperbolic differential equation systems. Sensitive here has multiple flavours: First, the formulation reduces the persistent memory footprint. This reduces pressure on the memory subsystem. Second, the formulation realises the underlying predictor-corrector scheme with single-touch semantics, i.e. each degree of freedom is...

The ADER approach is the extended Godunov-type schemes[1] which construct nonoscillatory explicit one-step schemes with very high order of accuracy in space and time by solving the DRPs (derivative Riemann problems). The ADER approach has been developed from the schemes for the linear scalar hyperbolic equations[2] to those for nonlinear multi-dimensional systems[3,4,5,6,7], and further to thos...

For problems defined in a two-dimensional domain Ω with boundary conditions specified on a curve Γ, we consider discontinuous Galerkin (DG) schemes with high order polynomial basis functions on a geometry fitting triangular mesh. It is well known that directly imposing the given boundary conditions on a piecewise segment approximation boundary Γh will render any finite element method to be at m...

The discontinuous Galerkin (DG) scheme is used to solve a conserved higher-order (CHO) traffic flow model by exploring several Riemann solvers. The second-order accurate DG scheme is found to be adequate in that the accuracy is comparable to the weighted essentially non-oscillatory (WENO) scheme with fifth-order accuracy and much better than the scheme with first-order accuracy in resolving a w...

We present a new line-based discontinuous Galerkin (DG) discretization scheme for firstand second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements, and it is closely related to the standard nodal DG scheme as well as several of its variants such as the collocation-based DG spectral element method (DGSEM) or...

Recent progress in applying the discontinuous Galerkin (DG) schemes for direct numerical simulation (DNS) and large eddy simulation (LES) of turbulent flows is attributed to the improvement in the stability and robustness of conventional methods. In particular, significant advances have been made with regard to the development of DG discretiza-tion for elliptic equations, including schemes of s...

A two-dimensional nonhydrostatic (NH) atmospheric model based on the compressible Euler system has been developed in the (x, z) Cartesian domain. The spatial discretization is based on a nodal discontinuous Galerkin (DG) method with exact integration. The orography is handled by the terrain-following heightbased coordinate system. The time integration uses the horizontally explicit and vertical...

We present a new numerical scheme which combines the Spectral Difference (SD) method up to arbitrary high order with \emph{a-posteriori} limiting using classical MUSCL-Hancock as fallback scheme. It delivers very accurate solutions in smooth regions of flow, while capturing sharp discontinuities without spurious oscillations. exploit strict equivalence between SD and Finite-Volume (FV) based on...