Analysis of low-pass filters for approximate deconvolution closure modelling in one-dimensional decaying Burgers turbulence

The idea of spatial filtering is central in approximate deconvolution large-eddy simulation (AD-LES) of turbulent flows. The need for low-pass filters naturally arises in the approximate deconvolution approach which is based solely on mathematical approximations by employing repeated filtering operators. Two families of low-pass spatial filters are studied in this paper: the Butterworth filters and the Padé filters. With a selection of various filtering parameters, variants of the AD-LES are systematically applied to the decaying Burgers turbulence problem, which is a standard prototype for more complex turbulent flows. Comparing with the direct numerical simulations, it is shown that all forms of the AD-LES approaches predict significantly better results than the under-resolved simulations at the same grid resolution. However, the results highly depend on the selection of the filtering procedure and the filter design. It is concluded that a complete attenuation for the smallest scales is crucial to prevent energy accumulation at the grid cut-off.     

A dynamic eddy-viscosity closure model for large eddy simulations of two-dimensional decaying turbulence

This paper puts forth a simplified dynamic eddy-viscosity subgrid-scale model for the vorticity transport equation which is employed in a large eddy simulation study of freely evolving isotropic two-dimensional turbulent flows. The dynamic parameter is averaged in space, thereby retrieving a spatially constant value which only varies in time. The proposed dynamic model is applied to a two-dimensional decaying turbulence problem in a square periodic box, which is a standard prototype of more realistic turbulent flows in the atmosphere and oceans, in order to eliminate any possible errors associated with the boundary conditions or mesh non-uniformities. Compared with high-resolution direct numerical simulations, the performance of the dynamic model is systematically investigated considering various filtering strategies by means of test filters. The effects of the computational resolution and the filtering ratio between the test and the grid filters are also studied by using a huge set of parameters.     

An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows

An unsteady incompressible Navier–Stokes solver that uses a dual time stepping method combined with spatially high‐order‐accurate finite differences, is developed for large eddy simulation (LES) of turbulent flows. The present solver uses a primitive variable formulation that is based on the artificial compressibility method and various convergence–acceleration techniques are incorporated to efficiently simulate unsteady flows. A localized dynamic subgrid model, which is formulated using the subgrid kinetic energy, is employed for subgrid turbulence modeling. To evaluate the accuracy and the efficiency of the new solver, a posteriori tests for various turbulent flows are carried out and the resulting turbulence statistics are compared with existing experimental and direct numerical simulation (DNS) data. Copyright © 1999 John Wiley & Sons, Ltd.     

A deconvolution‐based fourth‐order finite volume method for incompressible flows on non‐uniform grids

This paper is concerned with the development of a new high‐order finite volume method for the numerical simulation of highly convective unsteady incompressible flows on non‐uniform grids. Specifically, both a high‐order fluxes integration and the implicit deconvolution of the volume‐averaged field are considered. This way, the numerical solution effectively stands for a fourth‐order approximation of the point‐wise one. Moreover, the procedure is developed in the framework of a projection method for the pressure–velocity decoupling, while originally deriving proper high‐order intermediate boundary conditions. The entire numerical procedure is discussed in detail, giving particular attention to the consistent discretization of the deconvolution operation. The present method is also cast in the framework of approximate deconvolution modelling for large‐eddy simulation. The overall high accuracy of the method, both in time and space, is demonstrated. Finally, as a model of real flow computation, a two‐dimensional time‐evolving mixing layer is simulated, with and without sub‐grid scales modelling. Copyright © 2003 John Wiley & Sons, Ltd.     

A ghost-cell immersed boundary method for large eddy simulation of flows in complex geometries

An efficient ghost-cell immersed boundary (IB) method is proposed for large eddy simulations of three-dimensional incompressible flow in complex geometries. In the framework of finite volume method, the Navier–Stokes equations are integrated using an explicit time advancement scheme on a collocated mesh. Since the IB method is known to generate an unphysical velocity field inside the IB that violates the mass conservation of the cells near the IB, a new IB treatment is devised to eliminate the unphysical velocity generated near the IB and to improve the pressure distribution on the body surface. To validate the proposed method, both laminar and turbulent flow cases are presented. In particular, large eddy simulations were performed to simulate the turbulent flows over a circular cylinder and a sphere at subcritical Reynolds numbers. The computed results show good agreements with the published numerical and experimental data.     

A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes

We present a parallel fully implicit algorithm for the large eddy simulation (LES) of incompressible turbulent flows on unstructured meshes in three dimensions. The LES governing equations are discretized by a stabilized Galerkin finite element method in space and an implicit second-order backward differentiation scheme in time. To efficiently solve the resulting large nonlinear systems, we present a highly parallel Newton-Krylov-Schwarz algorithm based on domain decomposition techniques. Analytic Jacobian is applied in order to obtain the best achievable performance. Two benchmark problems of lid-driven cavity and flow passing a square cylinder are employed to validate the proposed algorithm. We then apply the algorithm to the LES of turbulent flows passing a full-size high-speed train with realistic geometry and operating conditions. The numerical results show that the algorithm is both accurate and efficient and exhibits a good scalability and parallel efficiency with tens of millions of degrees of freedom on a computer with up to 4096 processors. To understand the numerical behavior of the proposed fully implicit scheme, we study several important issues, including the choices of linear solvers, the overlapping size of the subdomains, and, especially, the accuracy of the Jacobian matrix. The results show that an exact Jacobian is necessary for the efficiency and the robustness of the proposed LES solver.     

A wavelet-based variational multiscale method for the LES of incompressible flows in a high-order DG-FEM framework

This work focuses upon the development of a wavelet-based variant of the variational multiscale method (VMS) for accurate and efficient large eddy simulation (LES) called wavelet-based VMS-LES (WMS-LES). This approach has been incorporated within the framework of a high-order incompressible flow solver based upon the pressure-stabilized discontinuous Galerkin finite element method (DG-FEM). The VMS approach is designed to produce an a priori scale separation of the governing equations, in a manner which makes no assumptions on either the boundary conditions or the mesh uniformity. Using second-generation wavelets (SGWs) elementwise for scale separation ensures, on one hand, the preservation of the computational compactness of the DG-FEM scheme and, on the other hand, the ability to achieve scale separation in wavenumber space. The optimal space-frequency localization property of the SGW provides an improvement over the commonly used Legendre polynomials. The suitability of the elementwise SGW scale-separation operation as a tool for error indication has been demonstrated in an h-adaptive computation of the reentrant corner test case. Finally, the DG-FEM solver and the WMS-LES method have been assessed through simulations upon the three-dimensional Taylor-Green vortex test case. Our results indicate that the WMS-LES approach exhibits a distinct improvement over the monolevel LES approach. This effect is not produced by a change in the magnitude of the subgrid dissipation but rather by the redistribution of the subgrid dissipation in wavenumber space.