Multi-rate time integration on overset meshes

In the computational fluid dynamic simulation of problems with complex geometries or multiscale spatio-temporal features, overset meshes can be effectively used. However, in the case of overset problems in which one or more of the meshes vary significantly in resolution, standard explicit time integrators limit the maximum allowable timestep across the entire simulation domain to that of the finest mesh, per the well-known Courant-Friedrichs-Lewy (CFL) condition. What therefore results is a potentially high amount of computational work that theoretically need not be performed on the grids with coarser resolution and a commensurately larger timestep. With the targeted use of multi-rate time integrators, separate meshes can be marched at independent rates in time to avoid wasteful computation while maintaining accuracy and stability. This work features the application of such integrators (specifically, multi-rate Adams-Bashforth (MRAB) integrators) to the simulation of overset mesh-described problems using a parallel Fortran code. The thesis focuses on the overarching mathematical theory, implementation via code generation, proof of numerical accuracy and stability, and demonstration of serial and parallel performance capabilities. Specifically, the results of this study directly indicate the numerical efficacy of MRAB integrators, outline a number of outstanding code challenges, demonstrate the expected reduction in time enabled by MRAB, and emphasize the need for proper load balancing through spatial decomposition in order for parallel runs to achieve the predicted time-saving benefit.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Aerospace Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Mikida, Cory

Contributors dc:contributor

• Bodony, Daniel J.
• Kloeckner, Andreas

• Multi-rate time integration
• Overset meshes
• Computational fluid dynamics

Statement dc:rights

• Copyright 2017 by Cory Mikida

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/97508

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/97508