Truly multi-dimensional all-speed schemes for the Euler equations on Cartesian grids

A discontinuous Galerkin method for solutions of the Euler equations on Cartesian grids with embedded geometries

We present a discontinuous Galerkin method (DGM) for solutions of the Euler equations on Cartesian grids with embedded geometries. Cartesian grid methods can provide considerable computational savings for computationally intensive schemes like the DGM. Cartesian mesh generation is also simplified compared to the body fitted meshes. However, cutting an embedded geometry out of the grid creates c...

Evaluation of the Lopatinski Determinant for Multi-dimensional Euler Equations

There is a large body of literature on the problem of stability for inviscid shock waves and in particular for gas dynamics, see [2, 17, 3, 5, 6, 9, 10, 16, 4, 7, 21, 12, 13, 1, 14, 15, 24]. The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function,” for the Euler equations of compressible gas dynamics. We describe two approaches to this problem. In the fir...

A parallel Newton-Krylov flow solver for the Euler equations on multi-block grids

We present a parallel Newton-Krylov algorithm for solving the three-dimensional Euler equations on multi-block structured meshes. The Euler equations are discretized on each block independently using second-order accurate summation-by-parts operators and scalar numerical dissipation. Boundary conditions are imposed and block interfaces are coupled using simultaneous approximation terms (SATs). ...

A I AA - 86 - 0 105 LU Implicit Schemes with Multiple Grids for the Euler Equations

The Discontinuous Galerkin Method on Cartesian Grids with Embedded Geometries: Spectrum Analysis and Implementation for Euler Equations

In this thesis, we analyze theoretical properties of the discontinuous Galerkin method (DGM) and propose novel approaches to implementation with the aim to increase its efficiency. First, we derive explicit expressions for the eigenvalues (spectrum) of the discontinuous Galerkin spatial discretization applied to the linear advection equation. We show that the eigenvalues are related to the subd...