Parallelisation of a Discontinuous Galerkin Solver for the Shallow Water Equation
نویسندگان
چکیده
This master’s thesis is concerned with the sequential and parallel implementations of a Discontinuous-Galerkin Solver for the shallow water equations in a newly developed framework using stacks. One of the other main aspects of the thesis is to keep a strong focus on memory efficiency using Sierpinski space-filling curves, which avoid redundant memory to keep the neighborhood information of the grid cells.
منابع مشابه
A dispersion-relation-preserving algorithm for a nonlinear shallow-water wave equation
The paper presents an iterative algorithm for studying a nonlinear shallow-water wave equation. The equation is written as an evolution equation, involving only first-order spatial derivatives, coupled with the Helmholtz equation. We propose a two-step iterative method that first solves the evolution equation by the implicit midpoint rule and then solves the Helmholtz equation using a three-poi...
متن کاملDiscontinuous/continuous Galerkin methods for coupling the primitive and wave continuity equations of shallow water
In this paper, we investigate a new approach for the numerical solution of the two-dimensional depth-integrated shallow water equations, based on coupling discontinuous and continuous Galerkin methods. In this approach, we couple a discontinuous Galerkin method applied to the primitive continuity equation, coupled to a continuous Galerkin method applied to the so-called ‘‘wave continuity equati...
متن کاملiHDG: An Iterative HDG Framework for Partial Differential Equations
We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and hence inheriting advances from both sides. In particular, the method can be viewed as a Gauss-Seidel approach that requires only independent element-by-element ...
متن کاملA Parallel High-Order Discontinuous Galerkin Shallow Water Model
The depth-integrated shallow water equations are frequently used for simulating geophysical flows, such as storm-surges, tsunamis and river flooding. In this paper a parallel shallow water solver using an unstructured high-order discontinuous Galerkin method is presented. The spatial discretization of the model is based on the Nektar++ spectral/hp library and the model is numerically shown to e...
متن کاملHigh-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations
An innovating approach is proposed to solve vectorial conservation laws on curved manifolds using the Discontinuous Galerkin Method. This new approach combines the advantages of the usual approaches described in the literature. The vectorial fields are expressed in a unit non-orthogonal local tangent basis derived from the polynomial mapping of curvilinear triangle elements, while the convectiv...
متن کامل