Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems required for the accurate transient modeling of systems involving electromagnetic waves in many emerging technologies. While Yees explicit, energy-conserving FDTD method is still prominent but restructed to structured grids and...

Discontinuous Galerkin Methods for the Shallow-Water Equations with bathymetric terms and dry areas

Shallow-Water Equations are encountered in many applications related to hydraulics, flood propagation or dam break problems. This set of nonlinear hyperbolic equations models a fluid flow in a domain where the depth of the fluid is much lower than its horizontal dimensions. Usually, these equations are treated using Finite Difference, Finite...

Stabilization of Kelvin-Helmholtz instabilities in 3D linearized Euler equations using a non-dissipative discontinuous Galerkin method

We present in this paper a time-domain Discontinuous Galerkin dissipation-free method for the transient solution of the three-dimensional linearized Euler equations around a steady-state solution. In the general context of a non-uniform supporting flow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic...