PDE-based Methods for Multiscale Computational Fluid Dynamics

Speaker: Raaghav Ramani, Department of Mathematics, University of California, Davis
September 14, 2023

Presentation

Abstract

We present a new numerical framework for simulating fluid flows in multiple space dimensions, and an associated set of algorithms that are (a) high-order accurate, (b) flexible and applicable to a variety of flow configurations, (c) highly efficient, running at least an order of magnitude faster than traditional solvers, and (d) simple to implement. Our methodology is founded upon a number of PDE-based modifications to the underlying fluid equations, including a nonlinear artificial viscosity stabilization technique, an asymptotic model for unstable interfaces, and a smooth dynamically adaptive mesh redistribution procedure. We will show a number of adaptive simulations of well-known and difficult gas dynamics problems, including strong shocks, unstable contact discontinuities, implosions, and shock-reflection and bounce-back. With the ability to smoothly “zoom-in” on and efficiently capture multiscale solution structures, we will demonstrate that our algorithms are able to provide an order of magnitude speed-up of low-resolution adaptive simulations over high-resolution uniform simulations for unstable Rayleigh-Taylor problems. This is joint work with Steve Shkoller at UC Davis.

Biography

Raag Ramani is a Ph.D. student in the Applied Mathematics department at UC Davis. His research focuses on the development of numerical algorithms for simulating fluid flows, including: high-resolution shock-capturing methods, adaptive meshing, multiscale modeling and simulation, vortex methods, and combustion & complex physics.

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