The present work joins a global effort in the development of efficient and accurate numerical tools for the simulation of complex fluid flows. More specifically, we focus on unsteady external flows, a fluid dynamics discipline which actually pervades applied sciences and engineering. These are the flow encountered in aircraft or car aerodynamics, wind energy, biological locomotion, etc. In the problems addressed here, we assume that the flow is incompressible and that the inertial forces dominate the viscous stresses: we are dealing with both moderate and high Reynolds number flows. Furthermore, the present work treats the flow equations in a very distinct approach. We use a vortex particle-mesh (VPM) method, which belongs to the broader class of “vortex methods”. Such methods use the vorticity-velocity formulation of the Navier-Stokes equations, rather than the velocity-pressure formulation: the vorticity field is thus the primary variable. The major advantage comes from the compactness of the vorticity field for external flows and wakes. A limited number of particles is thus required to discretize the entire flow. First, an immersed boundary technique has been developed and adapted to capture the flow past arbitrary shape bodies. The motivation is to benefit from the enhanced efficiency provided by the VPM method in terms of computational cost (as shown in previous works). The required Poisson equation is solved using an efficient grid-based solver combined with a parallel fast multipole method (which provides the required boundary conditions on each subdomain). Second, an accurate approach handling hierarchically refined meshes has been developed. We use both grid patches and particles of varying resolution. The originality of this work is the combination of the handling of multiple flow resolutions together with a full 3-D VPM Navier-Stokes solver to compute incompressible flows. This method also benefits from the versatility of the parallel fast multipole method which enables the efficient solution of the Poisson equation and straightforward domain decomposition. We have also demonstrated the potential of the mesh refinement technique on a Large-Eddy Simulation of a turbulent vortex wake rollup at very high Reynolds number.

(FSA 3)  – UCL, 2011

The recent advent of unstructured high order methods holds the promise of transforming industrial computational fluid dynamics practices. These novel methods combine high precision to high geometrical flexibility, but also provide excellent serial and parallel efficiency up to very large core counts. They also provide many possibilities for adaptive resolution, including accurate non-conformal connections and order adaptation. Due to the combination of these features, these methods are technically better suited for industrial scale resolving computations than the second order finite volume codes that pervade industrial CFD. As this type of computations will be required in the near future, and industrial simulation practices have not yet been firmly established, there is a unique window of opportunity to introduce these novel high-potential methods. Of these methods, the discontinuous Galerkin method is arguably the most mature, in terms of the theoretical framework, its practical deployment and applications. The main objective of this work is the development of this method for tackling scale-resolving simulations of turbomachinery flows. This thesis treats important practical and theoretical steps towards this goal. The first contribution is the study of the stability of the interior penalty method on hybrid meshes. Through the sharp computation of a trace inverse inequality, already available for simplex meshes, for all types of elements, and the generalisation of the coercivity analysis, optimal penalty parameters are found. In particular a specific variant for high aspect ratio meshes, typical for CFD, has been found. A further development concerns the definition of optimal data structures and assembly routines, based on the evaluation of computational performance of algebraic primitives. It has been shown how to define an extremely flexible matrix structure, whilst obtaining very high efficiency. By the reorganisation of assembly routines the increase of computational complexity with interpolation order is largely compensated higher computational efficiency. Both matrix-free GMRES and p-multigrid iterative strategies are furthermore implemented and compared. For the p-multigrid strategy, a generic framework is presented that provides high-quality transfer operators for h- and p-multigrid. Finally, a number of conceptual extensions to the DGM are proposed, namely the practical implementation of a non-conformal method for incompressible flows, as well as the application to frequential formulations, in particular of the Linearised Euler Equations including Perfectly Matched Layers. A first industrial CFD application is shown, which concerns the direct numerical simulation of transitional flow in a low pressure turbine cascade.

(FSA 3)  – UCL, 2013

Today, one of the major limitations of the finite element method remains its high computational cost. For that reason, mesh adaptivity has an important role to play since it provides a strong control of the distribution of the computational resources in time and space. Recently, mesh adaptivity has also become an interesting tool for the problems involving large displacements or deformations: industrial processes, fluid-structure interaction problems, crash simulations, biomedical applications, ... The classical node repositioning techniques do not always succeed in returning an acceptable mesh, and the solution that consists in re-meshing the domain suffers from important drawbacks (hardly parallelizable, global projections of the solution). This PhD dissertation focuses on the development of a mesh adaptation method able to handle arbitrarily large deformations of the computational domain. For that purpose, an approach combining a global node repositioning technique with local mesh modifications is chosen. The mesh adaptation methods based on local mesh modifications are first investigated in the framework of the two-phase flow problems. A method allowing large domain deformations is then proposed and evaluated. The approach is extended to meet some common requirements of the finite element analyses like the compatibility of the mesh to a CAD model and the handling of boundary layer meshes. The developments presented in this dissertation have been implemented in the open source library MAdLib, which is intended to fill a gap in the set of available open source softwares by providing efficient mesh adaptation capabilities for tetrahedral meshes.

(FSA 3)  – UCL, 2009

Predicting and understanding turbulent flows is still a partially open problem. This thesis is specifically focused on incompressible external aerodynamics. Lagrangian vortex element methods are well suited to simulate these type of flows but were limited to moderate Reynolds numbers. Here, hybrid approaches are proposed to overcome this limitation. First, flows that can be modeled using prescribed separation regions are investigated using simplified approaches. While they allow to handle high Reynolds number wake flows, only limited quantitative results can be obtained. Therefore, a new approach that combines an Eulerian grid-based solver and a Lagrangian solver is developed. This hybrid approach suppresses the biggest limitation of vortex methods: it allows to efficiently handle the boundary layer regions using the Eulerian solver. Another contribution is the development of a conservative redistribution scheme for hierarchically refined grids. It provides the required control on the spatial accuracy. The capabilities of the new scheme are demonstrated on the flow past a hemisphere at Re=3,000. Then, an application of vortex methods to a complex, turbulent, real-life problem is shown through the investigation of aircraft wake vortices in ground effect. The results light the path for future work: the developments made for the pure Lagrangian method should be transfered to the Vortex-In-Cell approach, as it is an order of magnitude faster. Finally, a hybrid RANS-LES turbulence modeling formulation is investigated and further adapted. While results are encouraging, the extension of the method to complex geometries is not trivial. Nevertheless, the core idea of the approach should be kept in mind as it could be adapted to more general RANS-LES approaches.

(FSA 3)  – UCL, 2006

Turbulent flows present structures with a wide range of scales. The computation of the complete physics of a turbulent flow (termed DNS) is very expensive and is, for the time being, limited to low and medium Reynolds number flows. As a way to capture high Reynolds number flows, a part of the physics complexity has to be modeled. Large eddy simulation (LES) is a simulation strategy where the large turbulent eddies present on a given mesh are captured and the influence of the non-resolved scales onto the resolved ones is modeled. The present thesis reports on the development and validation of a methodology in order to apply LES for complex wall-bounded flows. Discretization methods and LES models, termed subgrid scale models (SGS), compatible with such a geometrical complexity are discussed. It is proved that discrete a kinetic energy conserving discretization of the convective term is an attractive solution to perform stable simulations without the use of an artificial dissipation, as upwinding. The dissipative effect of the SGS model is thus unaffected by any additional dissipation process. The methodology is first applied to a developed parallel fourth-order incompressible flow solver for cartesian non-uniform meshes. In order to solve the resulting Poisson equation, an efficient multigrid solver is also developed. The code is first validated using DNS (Taylor-Green vortex, channel flow, four-vortex system) and LES (channel flow), and finally applied to the investigation of an aircraft two-vortex system in ground effect. The methodology is then applied to improve a RANS-based industrial unstructured compressible flow solver, developed at CENAERO, to perform well for LES applications. The proposed modifications are tested successfully on the unsteady flow past a sphere at Reynolds of 300 and 10000, corresponding to the subcritical regime.

(FSA 3) – UCL, 2007