Localized Artificial Viscosity Stabilization of Discontinuous Galerkin Methods for Nonhydrostatic Mesoscale Atmospheric Modeling

Localized Artificial Viscosity Stabilization of Discontinuous Galerkin Methods for Nonhydrostatic Mesoscale Atmospheric Modeling

Gibbs oscillation can show up near flow regions with strong temperature gradients in the numerical simulation of nonhydrostatic mesoscale atmospheric flows when using the high-order discontinuousGalerkin (DG) method. The authors propose to incorporate flow-feature-based localized Laplacian artificial viscosity in the DG framework to suppress the spurious oscillation in the vicinity of sharp the...

A Conservative Discontinuous Galerkin Semi-Implicit Formulation for the Navier-Stokes Equations in Nonhydrostatic Mesoscale Modeling

A Discontinuous Galerkin (DG) finite element formulation is proposed for the solution of the compressible Navier–Stokes equations for a vertically stratified fluid, which are of interest in mesoscale nonhydrostatic atmospheric modeling. The resulting scheme naturally ensures conservation of mass, momentum and energy. A semi-implicit time integration approach is adopted to improve the efficiency...

Continuous and discontinuous Galerkin methods for a scalable three-dimensional nonhydrostatic atmospheric model: Limited-area mode

This paper describes a unified, element based Galerkin (EBG) framework for a three-dimensional, nonhydrostatic model for the atmosphere. In general, EBG methods possess high-order accuracy, geometrical flexibility, excellent dispersion properties and good scalability. Our nonhydrostatic model, based on the compressible Euler equations, is appropriate for both limited-area and global atmospheric...

A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

We present spectral element (SE) and discontinuous Galerkin (DG) solutions of the Euler and compressible Navier– Stokes (NS) equations for stratified fluid flow which are of importance in nonhydrostatic mesoscale atmospheric modeling. We study three different forms of the governing equations using seven test cases. Three test cases involve flow over mountains which require the implementation of...

Taming nonlinear instability for discontinuous Galerkin scheme with artificial viscosity