Journal of Computational Physics
Journal of Computational Physics
The Lagrange-Galerkin spectral element method on unstructured quadrilateral grids
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Journal of Computational Physics
Runge–Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Journal of Scientific Computing
A semi-Lagrangian high-order method for Navier-Stokes equations
Journal of Computational Physics
A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods
SIAM Journal on Numerical Analysis
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations
Journal of Computational Physics
Parallel Implementation Issues: Global versus Local Methods
Computing in Science and Engineering
A three-dimensional spectral element model for the solution of the hydrostatic primitive equations
Journal of Computational Physics
Journal of Computational Physics
A nodal triangle-based spectral element method for the shallow water equations on the sphere
Journal of Computational Physics
Journal of Computational Physics
Spectral difference method for unstructured grids I: basic formulation
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
A spectral-element discontinuous Galerkin lattice Boltzmann method for nearly incompressible flows
Journal of Computational Physics
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Modeling and numerical approximation of a 2.5D set of equations for mesoscale atmospheric processes
Journal of Computational Physics
Journal of Computational Physics
Discontinuous Galerkin unsteady discrete adjoint method for real-time efficient tsunami simulations
Journal of Computational Physics
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
Simulations of moist convection by a variational multiscale stabilized finite element method
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.50 |
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 non-reflecting boundary conditions, while one test requires viscous terms (density current). Including viscous stresses into finite difference, finite element, or spectral element models poses no additional challenges; however, including these terms to either finite volume or discontinuous Galerkin models requires the introduction of additional machinery because these methods were originally designed for first-order operators. We use the local discontinuous Galerkin method to overcome this obstacle. The seven test cases show that all of our models yield good results. The main conclusion is that equation set 1 (non-conservation form) does not perform as well as sets 2 and 3 (conservation forms). For the density current (viscous), the SE and DG models using set 3 (mass and total energy) give less dissipative results than the other equation sets; based on these results we recommend set 3 for the development of future multiscale research codes. In addition, the fact that set 3 conserves both mass and energy up to machine precision motives us to pursue this equation set for the development of future mesoscale models. For the bubble and mountain tests, the DG models performed better. Based on these results and due to its conservation properties we recommend the DG method. In the worst case scenario, the DG models are 50% slower than the non-conservative SE models. In the best case scenario, the DG models are just as efficient as the conservative SE models.