Downloads & Free Reading Options - Results

We consider error estimates in weak parametrised norms for stabilized finite element approximations of the two-dimensional Navier-Stokes' equations. These weak norms can be related to the norms of certain filtered quantities, where the parameter of the norm, relates to the filter width. Under the assumption of the existence of a certain decomposition of the solution, into large eddies and fine scale fluctuations, the constants of the estimates are proven to be independent of both the Reynolds number and the Sobolev norm of the exact solution. Instead they exhibit exponential growth with a coefficient proportional to the maximum gradient of the large eddies. The error estimates are on a posteriori form, but using Sobolev injections valid on finite element spaces and the properties of the stabilization operators the residuals may be upper bounded uniformly, leading to robust a priori error estimates.

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.

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.

In this article we present recent developments in numerical methods for performing a Large Eddy Simulation (LES) of the formation and evolution of a wingtip vortex. The development of these vortices in the near wake, in combination with the large Reynolds numbers present in these cases, make these types of test cases particularly challenging to investigate numerically. We first give an overview of the Spectral Vanishing Viscosity--implicit LES (SVV-iLES) solver that is used to perform the simulations, and highlight techniques that have been adopted to solve various numerical issues that arise when studying such cases. To demonstrate the method's viability, we present results from numerical simulations of flow over a NACA 0012 profile wingtip at $Re_c = 1.2\cdot 10^6$ and compare them against experimental data, which is to date the highest Reynolds number achieved for a LES that has been correlated with experiments for this test case. Our model correlates favorably with experiment, both for the characteristic jetting in the primary vortex and pressure distribution on the wing surface. The proposed method is of general interest for the modeling of transitioning vortex dominated flows over complex geometries.

In this paper the accuracy and efficiency of a finite-volume multigrid solver for Large Eddy Simulation (LES) is investigated. The spatial discretization method employed is a second-order accurate central differencing scheme. For time discretization of the momentum equations the implicit second-order Crank-Nicolson method and the explicit second-order Adams-Bashforth method are considered. The influences of the two time discretizations, choice of grid size and time-step size and multigrid performance on the numerical accuracy and computational efficiency are discussed.

A numerical investigation of high-resolution schemes for solving the compressible Navier-Stokes equations in the context of Implicit Large Eddy Simulation (ILES) is presented. Computations have been performed using a hybrid total variation-diminishing (TVD) scheme. The hybrid TVD scheme combines third-order Godunov-type fluxes with first-order (dissipative) schemes using the flux limiters approach. Results are presented from numerical experiments of turbulent flow past an open cavity.