Implicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method

TL;DR

This paper introduces a high-order implicit large-eddy simulation method using the Interior Embedded Discontinuous Galerkin approach for efficient and accurate modeling of transitional turbulent compressible flows, demonstrating promising results over a compressor cascade.

Contribution

The paper develops a novel high-order ILES approach combining IEDG discretization with advanced nonlinear solvers for turbulent flow simulation, showing improved accuracy and efficiency.

Findings

High-order ILES results agree well with traditional LES models.

The approach uses fewer degrees of freedom than second-order methods.

High-order accuracy is crucial for predicting transitional turbulence.

Abstract

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method inherits the advantages of both the EDG method and the HDG method to make itself well-suited for turbulence simulations. We propose a minimal residual Newton algorithm for solving the nonlinear system arising from the IEDG discretization of the Navier-Stokes equations. The preconditioned GMRES algorithm is based on a restricted additive Schwarz (RAS) preconditioner in conjunction with a block incomplete LU factorization at the subdomain level. The proposed approach is applied to the ILES of transitional turbulent flows over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both design and off-design conditions. The high-order ILES results show good agreement with a subgrid-scale LES model discretized with a second-order finite volume code while using significantly less degrees of freedom. This work shows that high-order accuracy is key for predicting transitional turbulent flows without a SGS model.