Texas A&M Mathematics Graduate Student Organization

Next Talk:

Time: 4:45-5:45p, Monday, September 29

Location: Blocker 605AX

Speaker: Madison Sheridan

Title: A Robust Lagrangian Framework for Compressible Flow & Hyperelasticity

Abstract: Simulating compressible flow on a moving mesh is difficult: shocks, material interfaces, and large deformations can make high-order methods unstable or unphysical. I’ll present a high-order Lagrangian scheme that stays “within the laws of physics” by design. The core idea is simple: use a robust low-order update as a local reference, then limit the high-order update so it never leaves the admissible set—preserving mass locally, keeping density positive, and enforcing a minimum principle on internal energy. The method works with general equations of state (not just ideal gas) and can be dropped in to stabilize existing high-order schemes with minimal changes. I’ll also show how the same framework extends beyond fluids to nonlinear hyperelasticity (including anisotropic materials) while keeping the same physical guarantees. The talk will focus on the main construction and intuition, with brief theory highlights and examples (shock tubes, vortices, high-impact tests) illustrating both accuracy and robustness on distorted/curved meshes.