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 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 compressible Euler system, including a nonlinear artificial viscosity stabilization technique, an asymptotic model for unstable contact discontinuities, and a smooth dynamic adaptive mesh redistribution procedure.

We will show a number of adaptive simulations of well-known and difficult gas dynamics problems, including strong shocks and unstable contact discontinuities. With the ability for our algorithms to ​”zoom-in” on small-scale vortical structures, our algorithm is the first to provide a speed-up of low-resolution adaptive simulations over high-resolution uniform simulations of comparable quality for unstable Rayleigh-Taylor problems. This is joint work with Steve Shkoller at University of California, Davis.

Bio: Raag Ramani is a PhD student in the Applied Mathematics department at University of California, Davis.