Applied Math Seminar- High-Order Bound-Preserving Discontinuous Galerkin Methods for Reactive Flows and Euler Equations with Gravitation

Speaker:Fangyao Zhu, adjunct professor at Gogebic Community College.

When: Friday, February 20, 2026

Where: Where: Online zoom talk.

 

Title: High-Order Bound-Preserving Discontinuous Galerkin Methods for Reactive Flows and Euler Equations with Gravitation

 

Abstract: This talk presents high-order bound-preserving discontinuous Galerkin (DG) methods for nonlinear partial differential equations arising in non-equilibrium chemical reacting flows and the Euler equations with gravitational fields. A central challenge in both systems is maintaining physically meaningful solutions, particularly the positivity of density and pressure. For chemical reactive flows involving multiple species, the numerical scheme must also preserve the bounds of each mass fraction between zero and one while maintaining conservation. To address these requirements, we develop a bound-preserving DG method coupled with Patankar- type time integration, a conservative implicit approach designed for stiff source terms, to handle source terms efficiently. This framework maintains conservation, enforces physical bounds, and improves computational efficiency. For the Euler equations with gravitation, we further construct high-order well-balanced, positivity-preserving schemes capable of exactly maintaining steady states and accurately resolving small perturbations. Numerical experiments demonstrate the robustness and accuracy of the proposed methods.