Efficient Strong Stability Preserving Time Discretizations and Robust Automated Splitting for Time Evolution of Problems with Multiple Time-Scales

Abstract

Strong stability preserving (SSP) high order time discretizations were developed to ensure non-linear stability properties necessary in the numerical solution of hyperbolic partial differential equa-tions with discontinuous solutions. The research in the field of SSP methods centers around thesearch for high order SSP methods where the allowable time-step is as large as possible, per function evaluation required in each time-step.Of particular interest to us are equations that can be additively split into non-stiff (slow time-scale) and stiff (fast time-scale) components, where the stiff component is linear. In typical cases we find that when the SSP property is to be preserved, the overall time-step is limited by the stiff component even when specially designed methods such as implicit-explicit (IMEX) are used. The goal of this project is to develop efficient high order SSP time-stepping methods for multi-scale timestepping and also to develop efficient and automated optimal splitting to preserve stability.

Document Details

Document Type
DoD Grant Award
Publication Date
Aug 28, 2018
Source ID
FA95501810383

Entities

People

  • Sigal Gottlieb

Organizations

  • Air Force Office of Scientific Research
  • United States Air Force
  • University of Massachusetts

Tags

Readers

  • Computational Fluid Dynamics (CFD)
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)