Active Flux Methods for Compressible Flows: Flux Vector Splitting and Bound-Preservation

Speaker：Junming Duan (he Chinese University of Hong Kong，Shenzhen)

Time：2026-5-5 10:00

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value update incorporates the upwind idea but suffers from a stagnation issue for nonlinear problems due to inaccurate estimation of the upwind direction, and also from a mesh alignment issue partially resulting from decoupled point value updates. I will talk about using flux vector splitting for the point value update, offering a natural and uniform remedy to the two issues. To improve robustness, I will also talk about bound-preserving (BP) AF methods for hyperbolic conservation laws, with applications to the compressible Euler equations and ideal magnetohydrodynamics. A shock sensor-based limiting will be discussed for suppressing oscillations.