Construction of High-Order and Exact Pressure Equilibrium Schemes for Arbitrary Equations of State

AMS Seminar Series

Speaker: Christopher DeGrendele, Computational Aerosciences Branch, NASA Advanced Supercomputing Division
December 18, 2025

Presentation

Seminar Slide Deck (PDF-3.2MB)

Abstract

Typical fully conservative discretizations of the Euler compressible single or multi-component fluid equations governed by a real-fluid equation of state exhibit spurious pressure oscillations due to the nonlinearity of the thermodynamic relation between pressure, density, and internal energy. A fully conservative, pressure-equilibrium preserving method and a high-order, fully conservative, approximate pressure-equilibrium preserving method are presented. Both methods are general and can handle an arbitrary equation of state and arbitrary number of species. Unlike existing approaches to discretize the multi-component Euler equations, we do not introduce non conservative updates, overspecified equations, or design for a specific equation of state. The proposed methods are demonstrated on inviscid smooth interface advection problems governed by three equations of state: ideal-gas, stiffened-gas, and van der Waals where we show orders of magnitude reductions in spurious pressure oscillations compared to existing schemes.c

Biography

Chris DeGrendele is a computational scientist in the Computational Aerosciences Branch of the NASA Advanced Supercomputing Division at NASA Ames Research Center. He joined NASA through the Pathways Program in 2022 and is a member of the Launch, Ascent, and Vehicle Aerodynamics (LAVA) group, where he works primarily on launch environment simulations and numerical methods for multispecies and multiphase flow. He earned his Ph.D. in Applied Mathematics from the University of California, Santa Cruz (2025), and a B.S. in Physics and Astronomy from Stony Brook University (2020).

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