Identifier: 2009-32
Author(s): H. Riedmann
Title: Efficient numerical treatment of the compressible Navier-Stokes equations with nodal discontinuous Galerkin methods on graphics processors
Page count: 98 pp.
Date: 2009-10-13
Abstract:
In this work, the GPU implementation of a solver for the Euler and compressible Navier-Stokes equations on is described. The applied numerical scheme is a nodal discontinuous Galerkin method. This method parallelizes very well because the solution of a grid cell only depends on the solutions of its direct neighbors. The research code Hedge, in which the solver is implemented, makes use of this property by being able to run on graphics processors. Graphics processors can perform thousands of operations in parallel, i.e. at the same time, and therefore reach higher computation speeds than CPUs if used in the right way. This is assured by the already existing infrastructure of Hedge and will not be discussed in detail. Instead, the focus of this work lies on the implementation of the operator for the compressible Navier-Stokes equations and on testing this implementation for both correctness and performance. In order to solve the compressible Navier-Stokes equations, the first milestone is to solve the Euler equations which describe inviscid flow and therefore present a special case of the compressible Navier-Stokes equations. The correctness of the Euler solver is validated via a convergence analysis. Then it is upgraded to a solver for both the Euler and compressible Navier-Stokes equations. The convergence of the Navier-Stokes solver is also being analyzed. The results of both tests are presented in this work. At this point, we get a first sense of the possible speedup that the graphics processors offer in comparison to the CPU. After the validation of the solver, additional test cases are evaluated to examine the per- formance of the code running on graphics processors. Therefore, the mesh generation as well as the prescription of boundary conditions is being discussed. A two-dimensional test case simulating the flow past a square and the three-dimensional analog simulat- ing the flow past a cube are shown. Besides, a two-dimensional steady-state test case simulating the flow past an airfoil is displayed.
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