10 papers
Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems
Akshay Thakur, Sawan Kumar, Matthew Zahr +1
Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discreti…
Neural network-based Godunov corrections for approximate Riemann solvers using bi-fidelity learning
Akshay Thakur, Matthew J. Zahr
The Riemann problem is fundamental in the computational modeling of hyperbolic partial differential equations, enabling the development of stable and accurate upwind schemes. While…
An -adaptive method for accurate resolution of shock-dominated viscous flow based on implicit shock tracking
Huijing Dong, Masayuki Yano, Tianci Huang +1
This work introduces an optimization-based -adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order…
Model reduction of convection-dominated viscous conservation laws using implicit feature tracking and landmark image registration
Victor Zucatti, Matthew J. Zahr
Reduced-order models (ROMs) remain generally unreliable for convection-dominated problems, such as those encountered in hypersonic flows, due to the slowly decaying Kolmogorov -…
An implicit shock tracking method for simulation of shock-dominated flows over complex domains using mesh-based parametrizations
Alexander M. Perez Reyes, Matthew J. Zahr
A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided d…
A sharp-interface discontinuous Galerkin method for simulation of two-phase flow of real gases based on implicit shock tracking
Charles Naudet, Brian Taylor, Matthew J. Zahr
We present a high-order, sharp-interface method for simulation of two-phase flow of real gases using implicit shock tracking. The method is based on a phase-field formulation of tw…