Session: 2.1 - Recent development in CFD and Verification and Validation methods

Paper Number: 158472

158472 - Development and Verification of Finite Volume and Finite Element Solvers for Multi-Species Flow Simulations 

Abstract: 

Aerothermochemistry plays a crucial role in the design of reentry and hypersonic vehicles. In the high-enthalpy environment, such a vehicle is subjected to strong discontinuities in the flow field along with the chemical dissociation and ionization that affect the vehicle performance and heating. Accurate computational analysis of such multi-physics phenomena is a challenging task due to numerical difficulties such as carbuncle, stiffness due to extremely short time scale of the turbulence and reactions. Further, most of the state-of-the-art solvers for aerothermochemical analysis use second-order finite volume discretization schemes which suffer from excessive dissipation. The need for higher order numerical schemes grew bigger as the value of accuracy increases in hypersonic flow regime, especially when multiple chemical species are taken into consideration.
The finite element method, specifically the discontinuous Galerkin method, has been shown to not only produce accurate results when applied to fluid dynamics, but also handle complex geometries. However, this method suffers from instabilities in presences extreme shockwaves and other large gradients. This work documents the development of two multi-species solvers, one is based on finite volume formulation that uses fourth order skew-symmetric flux, and the other formulated according to the discontinuous Galerkin finite element method. Both the solvers are implemented using Loci auto-parallelizing framework.
In this paper, we present the results of the validation benchmark tests performed on the two solvers. The accuracy and the performance (computational cost) of each solver was assessed for each test, such as the Taylor-Green Vortex and the isentropic vortex advection cases. Furthermore, the ability of the schemes to capture shocks alongside with their stability relative to large gradients were carefully examined through shock tube tests and a multi-species underexpanded jet case.

Presenting Author: Asmaa Chakir Mississippi State University

Presenting Author Biography: