Arpit Babbar presents his work at the Indo-German Workshop on Hardware-aware Scientific Computing (IGHASC)

Arpit Babbar will present some of his PhD work at the Indo-German Workshop on Hardware-aware Scientific Computing (IGHASC) in Heidelberg.

Arpit Babbar’s talk

Admissibility preserving Lax-Wendroff Flux Reconstruction schemes for compressible flows

Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. 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 MPI efficient. Since solutions to hyperbolic conservation laws often contain shocks, in this work, we develop a subcell based limiter by blending LWFR with a lower order scheme, either first order finite volume or MUSCL-Hancock scheme. While the blending with a lower order scheme helps to control oscillations, it may not guarantee admissibility of discrete solution, e.g., positivity property of quantities like density and pressure. By exploiting the subcell structure and admissibility of lower order schemes, we devise a strategy to ensure that the blended scheme is admissibility preserving for the mean values and then use a scaling limiter to obtain admissibility of the polynomial solution. For MUSCL-Hancock scheme on non-cell-centered subcells, we develop a slope limiter, time step restrictions and suitable blending of higher order fluxes, that ensures admissibility of lower order updates and hence that of the cell averages. By using the MUSCL-Hancock scheme on subcells and Gauss-Legendre points in flux reconstruction, we improve small-scale resolution compared to the subcell-based RKDG blending scheme with first order finite volume method and Gauss-Legendre-Lobatto points. We demonstrate the performance of our scheme on compressible Euler’s equations, showcasing its ability to handle shocks and preserve small-scale structures.