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

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.Comment: 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201

Challenges for time and frequency domain aeroacoustic solvers

The linearized Euler equations (LEE) model acoustic propagation in the presence of rotational mean flows. They can be solved in time [1–3] or in frequency [4–6] domain, with both approaches having advantages and disadvantages. Here, those pros and cons are detailed, both from a modeling and a numerical/computational perspective. Furthermore, a performance comparison and cross-validation between two frequency and time domain state-of-the-art solvers is performed. The frequency domain solutions are obtained with the hybridizable discontinuous Galerkin (HDG) [7–12] and the embedded discontinuous Galerkin (EDG) [13–15] method, while the time domain solver is an explicit discontinuous-Galerkin based solver [1]. The performance comparison and cross-validation is performed on a problem of industrial interest, namely acoustic propagation from a duct exhaust in the presence of realistic mean flow.Peer ReviewedPostprint (published version

Rellich-type Discrete Compactness for Some Discontinuous Galerkin FEM

We deduce discrete compactness of Rellich type for some discontinuous Galerkin finite element methods (DGFEM) including hybrid ones, under fairly general settings on the triangulations and the finite element spaces. We make use of regularity of the solutions to an auxiliary second-order elliptic boundary value problem as well as the error estimates of the associated finite element solutions. The present results can be used for analyzing DGFEM applied to some boundary value and eigenvalue problems, and also to derive the discrete Poincar´e-Friedrichs inequalities.discontinuous Galerkin FEM, polygonal element, discrete compactness, Rellich’s selection theorem

Some Error Analysis on Virtual Element Methods

Some error analysis on virtual element methods including inverse inequalities, norm equivalence, and interpolation error estimates are presented for polygonal meshes which admits a virtual quasi-uniform triangulation

An embedded--hybridized discontinuous Galerkin finite element method for the Stokes equations

We present and analyze a new embedded--hybridized discontinuous Galerkin finite element method for the Stokes problem. The method has the attractive properties of full hybridized methods, namely an $H({\rm div})$-conforming velocity field, pointwise satisfaction of the continuity equation and \emph{a priori} error estimates for the velocity that are independent of the pressure. The embedded--hybridized formulation has advantages over a full hybridized formulation in that it has fewer global degrees-of-freedom for a given mesh and the algebraic structure of the resulting linear system is better suited to fast iterative solvers. The analysis results are supported by a range of numerical examples that demonstrate rates of convergence, and which show computational efficiency gains over a full hybridized formulation