Michel Lesoinne

Load and motion transfer algorithms for fluid/structure interaction problems with non-matching discrete interfaces: Momentum and energy conservation, optimal discretization and application to aeroelasticity

The prediction of many fluid/structure interaction phenomena requires solving simultaneously the coupled fluid and structural equations of equilibrium with an appropriate set of interface boundary conditions. In this paper, we consider the realistic situation where the fluid and structure subproblems have different resolution requirements and their computational domains have non-matching discrete interfaces, and address the proper discretization of the governing interface boundary conditions. We present and overview new and common algorithms for converting the fluid pressure and stress fields at the fluid/structure interface into a structural load, and for transferring the structural motion to the fluid system. We discuss the merits of these algorithms in terms of conservation properties and solution accuracy, and distinguish between theoretically important and practically significant issues. We validate our claims and illustrate our conclusions with several transient aeroelastic simulations.

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.

Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems

Abstract Partitioned procedures and staggered algorithms are often adopted for the solution of coupled fluid/structure interaction problems in the time domain. In this paper, we overview two sequential and parallel partitioned procedures that are popular in computational nonlinear aeroelasticity, and address their limitation in terms of accuracy and numerical stability. We propose two alternative serial and parallel staggered algorithms for the solution of coupled transient aeroelastic problems, and demonstrate their superior accuracy and computational efficiency with the flutter analysis of the AGARD Wing 445.6. We contrast our results with those computed by other investigators and validate them with experimental data.

Geometric conservation laws for flow problems with moving boundaries and deformable meshes, and their impact on aeroelastic computations

Abstract Numerical simulations of flow problems with moving boundaries commonly require the solution of the fluid equations on unstructured and deformable dynamic meshes. In this paper, we present a unified theory for deriving Geometric Conservation Laws (GCLs) for such problems. We consider several popular discretization methods for the spatial approximation of the flow equations including the Arbitrary Lagrangian-Eulerian (ALE) finite volume and finite element schemes, and space-time stabilized finite element formulations. We show that, except for the case of the space-time discretization method, the GCLs impose important constraints on the algorithms employed for time-integrating the semi-discrete equations governing the fluid and dynamic mesh motions. We address the impact of these constraints on the solution of coupled aeroelastic problems, and highlight the importance of the GCLs with an illustration of their effect on the computation of the transient aeroelastic response of a flat panel in transonic flow.

The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems

The FETI algorithms are a family of numerically scalable domain decomposition methods. They have been designed in the early 1990s for solving iteratively and on parallel machines, large-scale systems of equations arising from the finite element discretization of solid mechanics, structural engineering, structural dynamics, and acoustic scattering problems, and for analyzing complex structures obtained from the assembly of substructures with incompatible discrete interfaces. In this paper, we present the second generation of these methods that operate more efficiently on large numbers of subdomains, offer greater robustness, better performance, and more flexibility for implementation on a wider variety of computational platforms. We also report on the application and performance of these methods for the solution of geometrically non-linear structural analysis problems. We discuss key aspects of their implementation on shared and distributed memory parallel processors, benchmark them against optimized direct sparse solvers, and highlight their potential with the solution of large-scale structural mechanics problems with several million degrees of freedom.

Residual-Free Bubbles for the Helmholtz Equation

The Galerkin method enriched with residual-free bubbles is considered for approximating the solution of the Helmholtz equation. Two-dimensional tests demonstrate the improvement over the standard Galerkin method and the Galerkin-least-squares method using piecewise bilinear interpolations.

A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems

Summary. We present a Lagrange multiplier based two-level domain decomposition method for solving iteratively large-scale systems of equations arising from the finite element discretization of high-frequency exterior Helmholtz problems. The proposed method is essentially an extension of the regularized FETI (Finite Element Tearing and Interconnecting) method to indefinite problems. Its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix, and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves. We show numerically that the proposed method is scalable with respect to the mesh size, the subdomain size, and the wavenumber. We report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements.

Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems

We present two different but related Lagrange multiplier based domain decomposition (DD) methods for solving iteratively large-scale systems of equations arising from the finite element discretization of high-frequency exterior Helmholtz problems. The proposed methods are essentially two distinct extensions of the regularized finite element tearing and interconnecting (FETI) method to indefinite or complex problems. The first method employs a single Lagrange multiplier field to glue the local solutions at the subdomain interface boundaries. The second method employs two Lagrange multiplier fields for that purpose. The key ingredients of both of these FETI methods are the regularization of each subdomain matrix by a complex lumped mass matrix defined on the subdomain interface boundary, and the preconditioning of the global interface problem by a coarse second-level problem constructed with planar waves. We show numerically that both methods are scalable with respect to the mesh size, the subdomain size, and the wavenumber, but that the FETI method with a single Lagrange multiplier field – labeled FETI-H (H for Helmholtz) in this paper – delivers superior computational performances. We apply the FETI-H method to the parallel solution on a 24-processor Origin 2000 of an acoustic scattering problem with a submarine shaped obstacle, and report performance results that highlight the unique efficiency of this DD method for the solution of high frequency acoustic scattering problems.

Application of the FETI method to ASCI problems—scalability results on 1000 processors and discussion of highly heterogeneous problems

We report on the application of the one-level FETI method to the solution of a class of structural problems associated with the Department of Energys Accelerated Strategic Computing Initiative (ASCI). We focus on numerical and parallel scalability issues,and discuss the treatment by FETI of severe structural heterogeneities. We also report on preliminary performance results obtained on the ASCI Option Red supercomputer configured with as many as one thousand processors, for problems with as many as 5 million degrees of freedom.

Higher-Order Subiteration-Free Staggered Algorithm for Nonlinear Transient Aeroelastic Problems

The objective of this note is to present a new subiteration free implicit/implicit staggered algorithm that has the same computational complexity as the CSS procedure and yet delivers a superior time accuracy that is similar to that of a monolithic implicit scheme or a strongly coupled (full subiterations) partitioned method. Hence, this algorithm retains the computational efficiency and implementation advantages of partitioned mthods while offering the higher time accuracy of fully coupled implicit schemes