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Abstract: 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. [Copyright &y& Elsevier]

Two methodologies for designing an arbitrary Lagrangian–Eulerian (ALE) time-integrator for the semi-discrete Navier–Stokes equations are reviewed. Each methodology consists of a different mathematical framework for extending to moving grids a numerical scheme originally developed for computational fluid dynamics (CFD) on fixed grids, while preserving its formal order of time-accuracy established on fixed grids. Given a favorite scheme for the solution on fixed grids of the discrete Navier–Stokes equations, each of these two mathematical frameworks can generate multiple ALE extensions that share the same order of time-accuracy on moving grids. Typically, only a subset of these ALE schemes satisfy their respective discrete geometric conservation laws (DGCLs). Next, using a nonlinear scalar conservation law (NSCL) as a model problem, it is proved that satisfying the corresponding DGCL is a necessary condition for any ALE scheme to preserve on moving grids the nonlinear stability properties of its fixed-grid counterpart. Using the same NSCL, it is also proved that for the ALE extension of the second-order time-accurate trapezoidal rule, the DGCL requirement is a necessary as well as sufficient condition for nonlinear stability on moving grids. Hence, each of the two mathematical frameworks described in this paper combined with the DGCL test provides a general methodology for designing a robust ALE time-integrator for the solution of unsteady flow problems on dynamic meshes. As an example, the ALE extension of the popular three-point backward difference scheme is discussed in details. The corresponding theoretical results are illustrated with its application to the solution of various unsteady flow problems arising from the vibrations of the AGARD Wing 445.6 as well as a complete F-16 configuration in transonic airstreams. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

An overview is given of recent advances in a three-field methodology for modeling and solving nonlinear fluidstructure 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. [ABSTRACT FROM AUTHOR]

Presents information on a study which investigated the performance of Newton-Krylov methods applied to the solution of compressible high Reynolds number flows around two-dimensional geometries. Spatial discretization; Implicit time integration; Conclusions.

Abstract: Standard numerical methods used to solve the Reynolds averaged Navier–Stokes equations are known to be too dissipative to carry out large eddy simulations since the artificial dissipation they introduce to stabilize the discretization of the convection term usually interacts strongly with the subgrid scale model. A possible solution is to resort to non-dissipative central schemes. Unfortunately, these schemes are in general unstable. A way to reach stability is to select a central scheme that conserves the discrete kinetic energy. To that purpose, a family of kinetic energy conserving schemes is developed to perform simulations of compressible shock-free flows on unstructured grids. A direct numerical simulation of the flow past a sphere at a Reynolds number of 300 and a large eddy simulation at a Reynolds number of 10,000 are performed to validate the methodology. [Copyright &y& Elsevier]

Abstract: A methodology for designing formally second-order time-accurate and yet loosely-coupled partitioned procedures for the solution of nonlinear fluid–structure interaction (FSI) problems on moving grids is presented. Its key components are a fluid time-integrator that is provably second-order time-accurate on moving grids, the midpoint rule for advancing in time the solution of the structural dynamics equations of motion, a second-order structure predictor for bypassing the inner-iterations encountered in strongly-coupled solution procedures, and a carefully designed algorithm for time-integrating the motion of the fluid-mesh. Following this methodology, two different loosely-coupled schemes are constructed for the solution of transient nonlinear FSI problems and proved to be second-order time-accurate. Three-dimensional numerical results pertaining to the simulation of the aeroelastic response to a gravity excitation of a complete F-16 configuration are also presented. In addition to confirming the theoretical results discussed in this paper, these numerical results highlight a very stable behavior of the designed loosely-coupled partitioned procedures. [Copyright &y& Elsevier]