Development of a high-order discontinuous galerkin solver for internal combustion engine flows

Abstract

The aim of this work is to contribute to the development of an unstructured

ow solver able to match the increasing demand of the automotive industrial sector to advance CFD-aided design and analysis procedure. The method here presented is designed to ensure high-order of accuracy even in complex geometries using both explicit and implicit schemes for the temporal discretization of the compressible Reynolds Averaged Navier-Stokes (RANS) k-omega equations. The algorithm is based on the Discontinuous Galerkin (DG) nite element method, one of the most promising high-order methods, that combines excellent dispersion and dissipation properties with high geometrical exibility. The DG solver is based on di erent multi-stage explicit or many implicit or semi-implicit schemes for achieving high order accuracy in time. Here we focus on an implicit multi-stage multi-step method, known in the literature as Two Implicit Advanced Step-point (TIAS) method, analyzing the performance of the sixth-order accurate TIAS scheme for long time simulations of sti and non sti unsteady problems. The second objective of this work is to demonstrate the applicability and reliability of optimization algorithms to control spurious numerical oscillations in simulation of transonic ows. The proposed optimization strategy relies on the gradient based optimization approach employing an Automatic Di erentiation (AD) tool for the evaluation of the sensitivities. The optimization process acts directly on the shock capturing technique, seeking for the optimal values of the shock capturing parameters. The performance of the solver is demonstrated by solving several test-cases of direct relevance in the context of automotive and aerodynamic applications. The comparison between experimental/analytical and numerical results allowed the validation and/or revision of physical and numerical models implemented in the code. Finally, we remark that this work is the starting point of a larger investigation that aims to deal with ICE ow conditions that are poorly predicted by RANS approaches, such as ow separation and reattachment in a highly three-dimensional con guration, by using time-accurate integration of the DG space-discretized ILES and hybrid RANS-LES models.