High Order Strong Stability Preserving Time Discretizations for the Time Evolution of Hyperbolic Partial Differential Equations

Abstract

The objective of this project is to develop and analyze stable time discretizations suitable for the simulation of hyperbolic time-dependent partial differential equations. Implicit and explicit multi-step multi-stage time discretizations with optimal time-step restrictions have been developed, as well as implicit Runge--Kutta methods with downwinding and unconditional stability. A testing suite has been written to test some of these methods with a variety of spatial discretizations. New directions have been explored for implicit-explicit methods, which are useful for problems with convection and diffusion. Finally, novel provably stable multi-step time discretizations for use with Fourier pseudo-spectral spatial approximations of the three dimensional viscous Burgers equations and Navier-Stokes equations have been developed.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2012
Accession Number
ADA564549

Entities

People

  • Sigal Gottlieb

Organizations

  • University of Massachusetts Dartmouth

Tags

DTIC Thesaurus Topics

  • Air Force
  • Coefficients
  • Convection
  • Differential Equations
  • Diffusion
  • Diffusion Coefficient
  • Equations
  • Extrapolation
  • Interpolation
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Real Variables
  • Runge Kutta Method
  • Scientific Research
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)