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As application of computational fluid dynamics (CFD) technology grows from the simulation of flows around fixed and rigid obstacles to the prediction of flows past flexible and/or moving bodies, interest in CFD on dynamic meshes increases. This paper reviews some of the theoretical and computational advances made in this area, highlights sample applications they have enabled in aeroelasticity and multidisciplinary optimization, and concludes with a brief discussion of a specific barrier to progress. [ABSTRACT FROM AUTHOR]

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]

In this paper, a time-dependant calculation of flow in a lobe pump is presented. Calculations are performed using the arbitrary Lagrangean Eulerean (ALE) method. A grid manipulator is needed to move the nodes between time steps. The used grid manipulator is based on the pseudo-force idea. This means that each node is fictitiously connected with its 8 neighbours via fictitious springs. The equilibrium of the resulting pseudo spring forces defines the altered position of the nodes. The grid manipulator was coupled with a commercial flow solver and the whole was tested on the flow through a three-lobe lobe pump. Results were obtained for a rotational speed of 460 rpm and incompressible silicon oil as fluid. [ABSTRACT FROM AUTHOR]

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]

A Laplacian smoothing of the mesh velocities with variable diffusivity based on the distance from moving bodies is introduced. This variable diffusivity enforces a more uniform mesh velocity in the region close to the moving bodies. Given that in most applications these are regions where small elements are located, the new procedure decreases element distortion considerably, reducing the need for local or global remeshing, and in some cases avoiding it altogether. [ABSTRACT FROM AUTHOR]