Philippe Geuzaine

Application of a three-field nonlinear fluid–structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter

Abstract We overview a three-field formulation of coupled fluid–structure interaction problems where the flow is modeled by the arbitrary Lagrangian–Eulerian form of either the Euler or Navier–Stokes equations, the structure is represented by a detailed finite element (FE) model, and the fluid grid is unstructured, dynamic, and constructed by a robust structure analogy method. We discuss the latest advances in the computational algorithms associated with this approach for modeling aeroelastic problems. We apply the three-field nonlinear computational framework to the prediction of the aeroelastic frequencies and damping coefficients of an F-16 configuration in various subsonic, transonic, and supersonic regimes. We consider for this purpose both the popular two-dimensional typical wing section model and a detailed three-dimensional FE model of the structure, and compare in both cases the obtained numerical results with flight test data. We comment on the advantages and shortfalls of both approaches, and on the feasibility as well as the merit of the three-field formulation of nonlinear aeroelasticity for the extraction of flutter envelopes.

Aeroelastic Dynamic Analysis of a Full F-16 Configuration for Various Flight Conditions

An overview is given of recent advances in a three-field methodology for modeling and solving nonlinear fluid-structure interaction problems, and its application to the prediction of the aeroelastic frequencies and damping coefficients of a full F-16 configuration in various subsonic, transonic, and supersonic airstreams is reported. In this three-field methodology the flow is described by the arbitrary Lagrangian-Eulerian form of the Euler equations, the structure is represented by a detailed finite element model, and the fluid mesh is unstructured, dynamic, and updated by a robust torsional spring analogy method. Simulation results are presented for stabilized, accelerated, low-g, and high-g flight conditions, and correlated with flight-test data. Consequently, the practical feasibility and potential of the described computational-fluid-dynamics-based computational method for the flutter analysis of high-performance aircraft, particularly in the transonic regime, are discussed.

Design and analysis of ALE schemes with provable second-order time-accuracy for inviscid and viscous flow simulations

We consider the solution of inviscid as well as viscous unsteady flow problems with moving boundaries by the arbitrary Lagrangian-Eulerian (ALE) method. We present two computational approaches for achieving formal second-order time-accuracy on moving grids. The first approach is based on flux time-averaging, and the second one on mesh configuration time-averaging. In both cases, we prove that formally second-order time-accurate ALE schemes can be designed. We illustrate our theoretical findings and highlight their impact on practice with the solution of inviscid as well as viscous, unsteady, nonlinear flow problems associated with the AGARD Wing 445.6 and a complete F-16 configuration.

A stabilized finite element method using a discontinuous level set approach for the computation of bubble dynamics

A novel numerical method for solving three-dimensional two phase flow problems is presented. This method combines a quadrature free discontinuous Galerkin method for the level set equation with a pressure stabilized finite element method for the Navier Stokes equations. The main challenge in the computation of such flows is the accurate evaluation of surface tension forces. This involves the computation of the curvature of the fluid interface. In the context of the discontinuous Galerkin method, we show that the use of a curvature computed by means of a direct derivation of the level set function leads to inaccurate and oscillatory results. A more robust, second-order, least squares computation of the curvature that filters out the high frequencies and produces converged results is presented. This whole numerical technology allows to simulate a wide range of flow regimes with large density ratios, to accurately capture the shape of the deforming interface of the bubble and to maintain good mass conservation.

The Discrete Geometric Conservation Law and its Effects on Nonlinear Stability and Accuracy

Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to achieve nonlinear stability. We also show that the extension to moving grids of schemes that satisfy their DGCL requirement preserves the order of time-accuracy of their fixed-grid counterparts. Finally, we highlight the impact of these theoretical results on practical applications of computational fluid dynamics. A01-31Q91

Aeroacoustic simulation of the flow in a Helmholtz resonator

This paper reports on the application of a computational methodology for the simulation of aeroacoustics problems. An acoustic analogy is adopted and a in-house three-dimensional unstructured flow solver is coupled to theommercial finite element solver that uses a variational formulation of the Lighthill analogy. Numerical investigations are performed to study the noise radiated by a Helmholtz resonator placed in a duct.

Development and Study of Discretization Schemes on Sample Unstructured Grid Topologies for Large Eddy Simulation

Large eddy simulation (LES) on complex geometries by way of unstructured grids can be a tricky problem. As far as spatial discretization is concerned, it is well-known that standard Euler or Reynolds averaged Navier-Stokes (RANS) based schemes are too dissipative to perform LES since their numerical stabilization interacts strongly with the subgrid scale model. As, in the present approach, this spurious interaction is avoided, a low dissipation scheme has to be implemented. This scheme is built on a non-dissipative central scheme that conserves the discrete kinetic energy to reach stability. To prevent the generation of spurious numerical noise in underresolved non-turbulent parts of the simulation domain, a controlled amount of high order numerical dissipation is supplemented. As tetrahedra are reported to be suboptimal in regions where the grid stretching is large, discretization on hybrid meshes is also discussed. Finally, the present methodology is validated with DNS & LES applications.