Development of an implicit high-order Flux Reconstruction solver for high-speed flows on simplex elements

Abstract

In this seminar, we explore the frontiers of computational fluid dynamics through the lens of high-order Flux Reconstruction (FR) schemes, tailored for high-speed flow phenomena. The focus is on extending these schemes within the COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform to accommodate the intricate dynamics of high Mach number flows over both straight and curved-edged simplex elements. We delve into the intricacies of implementing the FR solver, highlighting its efficiency in accurately capturing complex flow features, even on coarser meshes, and its prowess in handling shock waves with fully implicit time marching procedure. The solver's capability extends to solving compressible flow problems, governed by Euler or Navier-Stokes equations, on triangular and tetrahedral meshes. We present extensive verification of the solver, showcasing its performance across a spectrum of flow speeds, culminating in hypersonic cases up to Mach 9.6. The solver's results, reaching up to 7^th, a.k.a P6, order accuracy for solution polynomials and 3^rd order, a.k.a Q2, for geometrical representation, have been compared with existing literature, demonstrating favorable outcomes.