Professor David Darmofal, Department of Aerospace, Texas
A&M University
Title:
Multigrid Methods for Convection-dominated Flows
Time:
4:00pm, Wednesday, October 2, 1996
Place:
503 Blocker
Abstract:
In this seminar, we will discuss recent advances in preconditioning
techniques for hyperbolic systems with particular emphasis on their
utility in multigrid methods. Our specific examples will be based
on the two-dimensional Euler equations, and the focus of this talk
will be local block preconditioners. In particular, we will study
two classes of local preconditioners: the discrete-based block
Jacobi preconditioner, and the continuum-based based local
preconditioners of Turkel and van Leer. Analysis of the low
frequency wave propagation characteristics of the Euler and
preconditioned Euler equations will be discussed. In particular, we
will show that the block Jacobi preconditioner does not effectively
reduce the spread of characteristic speeds especially for low Mach
number flows while the continuum-based local preconditioners
provide optimal wave speed equalization at all Mach numbers. The
performance of these preconditioners is compared for several tests
cases within a multigrid algorithm showing that the continuum-based
preconditioners result in much more effective multigrid algorithms
than the discrete block Jacobi preconditioners.