F. M. Denaro

Analysis of 3D backward‐facing step incompressible flows via a local average‐based numerical procedure

SUMMARY The study of the flow over a three-dimensional backward-facing step still provides interesting research when a new numerical method is developed and an investigation of the flow topology is performed. From a numerical point of view, accurate solutions are required, preferably with little computational effort, and the numerical results must lead to the understanding of the main features of the flow. The guidelines of an integrated framework are presented in this paper, starting with the description of the numerical methods for solving three-dimensional incompressible flows, based on a local-average procedure, up to the investigation of the flow structure by means of vortex lines reconstruction and vortices identification. Several results are reported concerning an analytical benchmark, simulation of flows in laminar and incipient transitional regimes and detection of vortical structures. Preliminary results for highly unsteady flows are also presented.

Scalable algebraic multilevel preconditioners with application to CFD

The solution of large and sparse linear systems is one of the main computational kernels in CFD applications and is often a very time-consuming task, thus requiring the use of effective algorithms on high-performance computers. Preconditioned Krylov solvers are the methods of choice for these systems, but the availability of “good” preconditioners is crucial to achieve efficiency and robustness. In this paper we discuss some issues concerning the design and the implementation of scalable algebraic multilevel preconditioners, that have shown to be able to enhance the performance of Krylov solvers in parallel settings. In this context, we outline the main objectives and the related design choices of MLD2P4, a package of multilevel preconditioners based on Schwarz methods and on the smoothed aggregation technique, that has been developed to provide scalable and easy-to-use preconditioners in the Parallel Sparse BLAS computing framework. Results concerning the application of various MLD2P4 preconditioners within a large eddy simulation of a turbulent channel flow are discussed.

On the Control of the Mass Errors in Finite Volume-Based Approximate Projection Methods for Large Eddy Simulations

Filtering in Large Eddy Simulation (LES) is often only a formalism since practically discretization of both the domain and operators is used as implicit grid-filtering to the variables. In the present study, the LES equations are written in the integral form around a Finite Volume (FV) Ώ rather than in the differential form as is more usual in Finite Differences (FD) and Spectral Methods (SM). Grid-filtering is therefore associated to the use of an explicit local volume average, by the way of surface flux integrals, and specific LES equations are here described. Moreover, since the filtered pressure characterizes itself only as a Lagrange multiplier used to satisfy the continuity constraint, projection methods are used for obtaining a divergence-free velocity. The choice of the non-staggered collocation is often preferable since is easily extendable on general geometries. However, the price to be paid in the so-called Approximate Projection Methods, is that the discrete continuity equation is satisfied only up to the magnitude of the local truncation error. Thus, the effects of such source errors are analyzed in FD and FV-based LES of turbulent channel flow. It will be shown that the FV formulation is much more efficient than FD in controlling the errors.

SParC-LES

We discuss the design and development of a parallel code for Large Eddy Simulation (LES) by exploiting libraries for sparse matrix computations. We formulate a numerical procedure for the LES of turbulent channel flows, based on an approximate projection method, in terms of linear algebra operators involving sparse matrices and vectors. Then we implement the procedure using general-purpose linear algebra libraries as building blocks. This approach allows to pursue goals such as modularity, accuracy and robustness, as well as easy and fast exploitation of parallelism, with a relatively low coding effort. The parallel LES code developed in this work, named SParC-LES (Sparse Parallel Computation-based LES), exploits two parallel libraries: PSBLAS, providing basic sparse matrix operators and Krylov solvers, and MLD2P4, providing a suite of algebraic multilevel Schwarz preconditioners. Numerical experiments, concerning the simulation by SParC-LES of a turbulent flow in a plane channel, confirm that the LES code can achieve a satisfactory parallel performance. This supports our opinion that the software design methodology used to build SParC-LES yields a very good tradeoff between the exploitation of the computational power of parallel computers and the amount of coding effort.

A new development of the dynamic procedure for the integral-based implicit filtering in large-eddy simulation

This paper is focused on the role of integral-based Finite Volume (FV) discretizations in Large Eddy Simulation of turbulence. The integral-based form implicitly induces the top-hat filtering on the balanced variable. This leads us to rewrite also a different decomposition of the fluxes. As a consequence, the development of a new Germano identity can be achieved having some advantages over the classical differential-based form. However, the dynamic procedure requires an explicit test-filtering on a computational grid that, to be optimal, requires an evaluation of the shape of the numerical filter induced by the FV-based discretization. Therefore, the goal of this paper is the theoretical study of the effective filter shape induced by some 3D Finite Volume reconstructions. The induced shape and width are analyzed by means of a modified wavenumber-like analysis that is applied in the 3D Fourier space. Some schemes are considered and the differences in terms of either velocity or flux interpolations on either staggered or non-staggered grids are derived and analyzed.