of “High-Performance High-Order Simulation of Wave and Plasma Phenomena” by Andreas Klöckner, Ph.D., Brown University, May 2010 This thesis presents results aiming to enhance and broaden the applicability of the discontinuous Galerkin (“DG”) method in a variety of ways. DG was chosen as a foundation for this work because it yields high-order finite element discretizations with very favorable nu...

Nowadays, the penetration of distributed generation (DG) in power networks takes special place worldwide and is increasing in developed countries. In order to improve voltage profile, stability, reduction of power losses etc, it is necessary that, this increasing of installation of DGs in distribution system should be done systematically. This paper introduces an optimal placement method in ord...

Discontinuous Galerkin (DG) methodsCompressible Navier–Stokes equations, compressible flow haveSpectral element method a long history in computational physics and engineering to approximate solutions of partial differential equations due their high-order accuracyAccuracy geometric flexibility. However, DG is not perfect there remain some issues. Concerning robustness, has undergone an extensive...

We construct a local Lax-Friedrichs type positivity-preserving flux for compressible Navier-Stokes equations, which can be easily extended to high dimensions for generic forms of equations of state, shear stress tensor and heat flux. With this positivity-preserving flux, any finite volume type schemes including discontinuous Galerkin (DG) schemes with strong stability preserving Runge-Kutta tim...

Turbulent compressible flows are traditionally simulated using explicit time integrators applied to discretized versions of the Navier-Stokes equations. However, associated Courant-Friedrichs-Lewy condition severely restricts maximum step size. Exploiting Lagrangian nature Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice method (SLL...

We present a splitting method for the one-dimensional Saint-Venant-Exner equations used describing bed evolution in shallow water systems. adapt flux vector approach of Toro and Vazquez-Cend\`on identify one subsystem conservative (advection system) non-conservative (pressure system), both having very simple eigenstructure compared to full system. The final numerical scheme is constructed using...

A numerical solution strategy for a one-dimensional field dislocation mechanics (FDM) model using the Discontinuous Galerkin (DG) method is developed. The FDM capable of simulating dynamics discrete, nonsingular dislocations partial differential equation involving conservation law Burgers vector content with constitutive input nucleation and velocity. Modeling individual lines an equilibrium co...

We introduce a novel local time-stepping technique for marching-in-time algorithms. The technique is denoted as Causal-Path Local Time-Stepping (CPLTS) and it is applied for two time integration techniques: fourth order low–storage explicit Runge–Kutta (LSERK4) and second order Leapfrog (LF2). The CPLTS method is applied to evolve Maxwell’s curl equations using a Discontinuous Galerkin (DG) sch...