We present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty proposed approach is use high-order discontinuous Galerkin (dG) schemes and shock-capturing Finite Volume (FV) scheme coupled via an $hp$ adaptive mesh refinement ($hp$-AMR) strategy that offers accurate resolution $hp$-AMR based on multi-level blo...

We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a strict maximum principle for general nonlinear convection-diffusion equations on unstructured triangular meshes. Motivated by genuinely high order maximum-principle-satisfying DG schemes for hyperbolic conservation laws [14, 26], we prove that under suitable time step restriction for forward Euler time stepping...

The possibility of using accurate numerical methods to simulate seismic wavefields on unstructured meshes for complex rheologies is explored. In particular, the Discontinuous Galerkin (DG) finite element method for seismic wave propagation is extended to the rheological types of viscoelasticity, anisotropy and poroelasticity. First is presented the DG method for the elastic isotropic case on te...

The multigrid method for discontinuous Galerkin discretizations of advection-diffusion problems is presented. It is based on a block Gauss-Seidel smoother with downwind ordering honoring the advection operator. The cell matrices of the DG scheme are inverted in this smoother in order to obtain robustness for higher order elements. Employing a set of experiments, we show that this technique actu...

This paper proposes an autonomous and economic droop control scheme for DC microgrid application. In this method, a cost-effective power sharing technique among various types of DG units is properly adopted. The droop settings are determined based on an algorithm to individually manage the power management without any complicated optimization methods commonly applied in the centralized control ...

We present a novel discretization method for nonlinear convection-diffusion equations and, in particular, for the compressible Navier-Stokes equations. The method is based on a Discontinuous Galerkin (DG) discretization for convection terms, and a mixed method using H(div) spaces for the diffusive terms. Furthermore, hybridization is used to reduce the number of globally coupled degrees of free...