Accession Number:

ADA564549

Title:

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

Descriptive Note:

Final rept. 1 Mar 2009-30 Nov 2011

Corporate Author:

MASSACHUSETTS UNIV DARTMOUTH DEPT OF MATHEMATICS

Personal Author(s):

• Gottlieb, Sigal

Report Date:

2012-02-01

Pagination or Media Count:

9.0

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.

Descriptors:

• *RUNGE KUTTA METHOD
• COMPUTATION SCIENCE
• NAVIER STOKES EQUATIONS
• OPTIMIZATION
• PARTIAL DIFFERENTIAL EQUATIONS

Subject Categories:

• Statistics and Probability
• Operations Research
• Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE