PhD Synopsis seminar by Arpit Babbar

Title 
Lax-Wendroff Flux Reconstruction for Compressible Flows

Abstract

The Lax-Wendroff method is a single step high order method for solving time dependent partial differential equations, in contrast to Runge-Kutta methods that need multiple stages per time step. The single step nature of the method enables evolution to the next time level with only one interface communication, making the method arithmetically intense and suitable for modern computing hardware. We develop a flux reconstruction version of the method for hyperbolic conservation laws with the following key developments.

•  The numerical flux is constructed to improve accuracy for nonlinear problems and obtain higher CFL numbers.

•  An admissibility preserving subcell limiter is developed with enhanced accuracy obtained using Gauss-Legendre solution points and MUSCL-Hancock reconstruction on subcells.

•  Extension to adaptively refined, curvilinear meshes is made. In such problems, Fourier stability analysis does not apply and thus an error based time stepping method is proposed.

The other developments involve applications to equations with source terms, a flux reconstruction variant of multiderivative Runge-Kutta methods which are a generalization to Lax-Wendroff and Runge-Kutta methods, and an extension to second order models like compressible Navier-Stokes equations.