Bruno Koobus

Torsional springs for two-dimensional dynamic unstructured fluid meshes

Abstract Dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries. They are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and/or deformations. In this paper, we propose to control the arbitrary motion of two-dimensional dynamic unstructured fluid grids with additional torsional springs. We show that such springs can be designed to prohibit the interpenetration of neighboring triangles, and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications. We illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness, quality, and performance.

Second-order time-accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes

Abstract We consider the solution of two- and three-dimensional flow problems with moving boundaries using the Arbitrary Lagrangian Eulerian formulation or dynamic meshes. We focus on the case where spatial discretization is performed by unstructured finite volumes and/or finite elements. We formulate the consequence of the Geometric Conservation Law on the second-order implicit temporal discretization of the semi-discrete equations governing such problems, and use it as a guideline to construct a new family of second-order time-accurate and geometrically conservative implicit numerical schemes for flow computations on moving grids. We apply these new algorithms to the solution of three-dimensional flow problems with moving and deforming boundaries, demonstrate their superior accuracy and computational efficiency, and highlight their impact on the simulation of fluid/structure interaction problems.

AN IMPROVED METHOD OF SPRING ANALOGY FOR DYNAMIC UNSTRUCTURED FLUID MESHES

Dynamic fluid grids are commonly used for the solution of flow problems with moving boundaries. They are often represented by a network of fictitious lineal springs that can become unreliable when the fluid mesh undergoes large displacements and/or deformations. In this paper, we propose to control the arbitrary motion of two-dimensional dynamic unstructured fluid grids with additional torsional springs. We show that such springs can be designed to prohibit the interpenetration of neighboring triangles, and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications. We illustrate our new dynamic mesh motion algorithm with several examples that highlight its advantages in terms of robustness, quality, and performance.

Reverse Automatic Differentiation for Optimum Design: From Adjoint State Assembly to Gradient Computation

Gradient descent is a key technique in Optimal Design problems. We describe a method to compute the gradient of a optimization criterion with respect to design parameters. This method is hybrid, using Automatic Differentiation to compute the residual of the adjoint system, and using this residual in a hand-written solver that computes the adjoint state and then the gradient. Automatic Differentiation is here used in its so-called reverse mode, with a special refinement for gather-scatter loops. The hand-written solver uses a matrix-free algorithm, preconditioned by the first-order derivative of the flux function. This method was tested on a typical optimal design problem, for which we give validation and performance results.

Positivity statements for a Mixed-Element-Volume scheme on fixed and moving grids

This paper considers a class of second-order accurate vertex centered mixed finite element finite-volume MUSCL schemes. These schemes apply to unstructured triangulations and tetrahedrizations and fluxes are computed on an edge basis. We define conditions under which these schemes satisfy a density-positivity statement for Euler flows, a maximum principle for a scalar conservation law and a multicomponent flow. This extends to an Arbitrary- Lagrangian-Eulerian formulation. Steady and unsteady flow simulations illustrate the accuracy and the robustness of these schemes.

Computation of unsteady viscous flows around moving bodies using the k-ε turbulence model on unstructured dynamic grids

Abstract We consider the numerical solution on unstructured dynamic meshes of the averaged Navier–Stokes equations equipped with the k – e turbulence model and a wall function. We discuss discretization issues pertaining to conservation laws, moving grids, and numerical dissipation. We also present a robust spring analogy method for constructing dynamic meshes. We validate our implementation of this two-equation turbulence model and justify its usage for a class of vortex shedding problems by correlating our computational results with experimental data obtained for a flow past a square cylinder. We also apply our solution methodology to the two-dimensional aerodynamic stability analysis of the Tacoma Narrows Bridge, and report numerical results that are in good agreement with observed data.

A scaled and minimum overlap restricted additive Schwarz method with application to aerodynamics

Abstract A variant of the classical additive Schwarz preconditioner (AS) is presented and applied to the solution of a general class of two- and three-dimensional flow problems. The scaled restricted additive Schwarz (RAS) with minimal overlap preconditioner is easy to parallelize since all the local communications among processors only involve information pertaining to the interface of the nonoverlapping subdomains. The new method is superior to AS and the Jacobi algorithm in terms of both iteration counts and CPU time, as well as the communication cost when implemented on distributed memory computers.

A STUDY OF LES MODELS FOR THE SIMULATION OF A TURBULENT FLOW AROUND A TRUSS SPAR GEOMETRY

A new generation of LES type model is used to simulate the flow around a Spar geometry. This new method involves a Variational Multiscale formulation, allowing better capture of the back scatter. This approach is well suited for flows where small scales transmit a notable amount of energy to larger ones. The flow simulation is compared with experimental data from a model test.Copyright

Parallel simulation of three-dimensional complex flows: Application to two-phase compressible flows and turbulent wakes

In this paper, we present parallel simulations of three-dimensional complex flows obtained on an ORIGIN 3800 computer and on homogeneous and heterogeneous (processors of different speeds and RAM) computational grids. The solver under consideration, which is representative of modern numerics used in industrial computational fluid dynamics (CFD) software, is based on a mixed element-volume method on unstructured tedrahedrisations. The parallelisation strategy combines mesh partitioning techniques, a message-passing programming model and an additive Schwarz algorithm. The parallelisation performances are analysed on a two-phase compressible flow and a turbulent flow past a square cylinder.

A methodology for the shape optimization of flexible wings

Purpose – To propose an integrated algorithm for aerodynamic shape optimization of aircraft wings under the effect of aeroelastic deformations at supersonic regime.Design/methodology/approach – A methodology is proposed in which a high‐fidelity aeroelastic analyser and an aerodynamic optimizer are loosely coupled. The shape optimizer is based on a “CAD‐free” approach and an exact gradient method with a single adjoint state. The global iterative process yields optimal shapes in the at‐rest condition (i.e. with the aeroelastic deformations substracted).Findings – The methodology was tested under different conditions, taking into account a combined optimization goal: to reduce the sonic boom production, while preserving the aerodynamic performances of flexible wings. The objective function model contains both aerodynamic parameters and an acoustic term based on the sonic boom downwards emission.Practical implications – This paper proposes a shape optimization methodology developed by researchers but aiming a...