Robust approximation of hyperbolic-dominated models.
Abstract
The objective of this proposal is to establish a rigorous research program for constructing robust time and space approximation methods for nonlinear conservation equations mixing hyperbolic, parabolic and elliptic effects with a dominating hyperbolic character. Many applications of importance to the Air Force and other agencies involve models mixing hyperbolicity with other physical effects such as diffusion and dispersion. The research program is articulated around the following five points- (i) The numerical methods must preserve convex invariant domains of the problem on any unstructured meshes in any space dimension; (ii) The methods must be provably robust- they should not involve any tuning parameter, mesh-dependent coefficient, or problem-dependent stabilization. They should be easy to program and parallelize. They should not require any subtle mathematical knowledge from practitioners; (iii) The methods should be at least third-order accurate in space and time and must be open to higher-order extensions; (iv) The methods should respect physical dissipation mechanisms; (v) The above objectives must be reached by stating precise statements supported either by mathematical proofs or very strong numerical evidences. These goals will be achieved under realistic time stepping constraints (i.e., the explicit hyperbolic CFL instead of the explicit parabolic CFL). A key originality of this project is that the numerical methods are provably robust.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 22, 2024
- Source ID
- FA95502310007
Entities
People
- Jean-luc Guermond
Organizations
- Air Force Office of Scientific Research
- Texas A&M University
- United States Air Force