Optimization and validation of discontinuous Galerkin Code for the 3D Navier-Stokes equations

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2011.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 165-170).From residual and Jacobian assembly to the linear solve, the components of a high-order, Discontinuous Galerkin Finite Element Method (DGFEM) for the Navier-Stokes equations in 3D are presented. Emphasis is given to residual and Jacobian assembly, since these are rarely discussed in the literature; in particular, this thesis focuses on code optimization. Performance properties of DG methods are identified, including key memory bottlenecks. A detailed overview of the memory hierarchy on modern CPUs is given along with discussion on optimization suggestions for utilizing the hierarchy efficiently. Other programming suggestions are also given, including the process for rewriting residual and Jacobian assembly using matrix-matrix products. Finally, a validation of the performance of the 3D, viscous DG solver is presented through a series of canonical test cases.by Eric Hung-Lin Liu.S.M