Two-dimensional driven cavity flows with the Reynolds number ranging from 10 2 to 3.2 x 10 3 are used to assess the performance of second-order upwind and central difference schemes for the convection terms. Three different implementations of the second-order upwind scheme are designed and tested in the context of the SIMPLE algorithm, with the grid size varying from 21 x 21 to 161 x 161 uniformly spaced nodes. Converged solutions are obtained for all Reynolds numbers. Although these different implementations of the second-order upwind scheme have the same formal order of accuracy, significant differences in numerical accuracy are observed. It is demonstrated that better performance can be obtained for the second-order upwind scheme if the discretization is cast in accordance with the finite volume formulation. Although both the second-order upwind and central difference schemes exhibit no oscillations in the solution, the upwind scheme is more accurate. In assessing and comparing the performance of these schemes, the distribution of cell Reynolds number is discussed and its impact on numerical accuracy illustrated.

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SUMMARYA new ÿnite volume method for the incompressible Navier-Stokes equations, expressed in arbitrary Lagrangian-Eulerian (ALE) form, is presented. The method uses a staggered storage arrangement for the pressure and velocity variables and adopts an edge-based data structure and assembly procedure which is valid for arbitrary n-sided polygonal meshes. Edge formulas are presented for assembling the ALE form of the momentum and pressure equations. An implicit multi-stage time integrator is constructed that is geometrically conservative to the precision of the arithmetic used in the computation. The method is shown to be second-order-accurate in time and space for general time-dependent polygonal meshes. The method is ÿrst evaluated using several well-known unsteady incompressible Navier-Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem. Published in

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This paper focuses on the validation of a new all-speed Computational Fluid Dynamics (CFD) code called Loci-STREAM. This computational package is not just another CFD solver; rather, it integrates proven numerical methods and state-of-the-art physical models to compute all-speed flows using generalized grids in a novel rule-based programming framework called Loci which allows: (a) seamless integration of multidisciplinary physics in a unified manner, and (b) automatic handling of massively parallel computing. The objective is to be able to routinely simulate problems involving complex geometries requiring large unstructured grids with arbitrary polyhedral cells and complex multidisciplinary physics. As a first step towards achieving this objective, a wide range of model test cases are studied here, including incompressible laminar and turbulent flow cases, inviscid compressible flow cases, compressible turbulent flows with wall heat transfer as well as internal turbulent flows in 3D geometries and unsteady computations. Comparison of the code with experimental and prior benchmark numerical results is done to validate the robustness of the code for flows ranging from incompressible to supersonic regimes. A scalability analysis is performed as well to study the efficiency of parallelization.