Robust and Accurate Approximation of Hyperbolic Systems
Abstract
Research objectives: The project consists of developing robust numerical methods for solving hyperbolic systems of conservation laws such as the compressible Euler equations and radiative hydrodynamics. Most current high-order numerical methods are unattractive to practitioners because they are not robust. Our research program consists of developing numerical methods with the following properties, all related to robustness: (i) be invariant domain preserving on any unstructured meshes in any space dimension; (ii) do not involve any tuning parameters, mesh-dependent or problem-dependent stabilizations (no subtle mathematical knowledge should be required from practitioners to use these methods); (iii) beat least third-order accurate in space and time and be open to higher-order extensions; (iv) be consistent with physical dissipation mechanisms. The above objectives will be reached by stating precise statements supported either by mathematical proofs or very strong numerical evidences. Technical approaches: We propose to use the first-order invariant domain preserving method we have developed in the previous grant period as a robust basis for a high order method constructed by adding a dissipation proportional to the local violation of the second-principle of thermodynamics. Since all high-order techniques develop un-physical oscillations (by Godunov's theorem), we are going to correct these oscillations by identifying a proper local admissible convex domain where the solution must stay
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 11, 2021
- Accession Number
- AD1153241
Entities
People
- Jean-luc Guermond
Organizations
- Texas A&M University