Title page for ETD etd-314610359611541

Type of Document Dissertation
Author Bruner, Christopher William Stuteville
URN etd-314610359611541
Title Parallelization of the Euler Equations on Unstructured Grids
Degree PhD
Department Aerospace and Ocean Engineering
Advisory Committee
Advisor Name Title
Devenport, William L.
Grossman, Bernard M.
Hoeg, Joseph G.
Schetz, Joseph A.
Walters, Robert W. Committee Chair
  • unstructured grids
  • parallel algorithms
  • computational fluid dynamics
Date of Defense 1996-05-01
Availability unrestricted
Several different time-integration

algorithms for the Euler equations are

investigated on two

distributed-memory parallel computers

using an explicit message-passing

paradigm: these are classic Euler

Explicit, four-stage Jameson-style

Runge-Kutta, Block Jacobi, Block

Gauss-Seidel, and Block Symmetric

Gauss-Seidel. A finite-volume

formulation is used for the spatial

discretization of the physical domain.

Both two- and three-dimensional test

cases are evaluated against five

reference solutions to demonstrate

accuracy of the fundamental sequential

algorithms. Different schemes for

communicating or approximating data

that are not available on the local

compute node are discussed and it is

shown that complete sharing of the

evolving solution to the inner matrix

problem at every iteration is faster than

the other schemes considered.

Speedup and efficiency issues

pertaining to the various

time-integration algorithms are then

addressed for each system. Of the

algorithms considered, Symmetric

Block Gauss-Seidel has the overall

best performance. It is also

demonstrated that using parallel

efficiency as the sole means of

evaluating performance of an algorithm

often leads to erroneous conclusions;

the clock time needed to solve a

problem is a much better indicator of

algorithm performance. A general

method for extending one-dimensional

limiter formulations to the unstructured

case is also discussed and applied to

Van Albada's limiter as well as Roe's

Superbee limiter. Solutions and

convergence histories for a

two-dimensional supersonic ramp

problem using these limiters are

presented along with computations

using the limiters of Barth & Jesperson

and Venkatakrishnan--the Van

Al-bada limiter has performance

similar to Venkatakrishnan's.

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