A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

A parallel meshless dynamic cloud method on graphic processing units for unsteady compressible flows past moving boundaries

This paper presents an effort to implement a recently proposed meshless dynamic cloud method (Hong Wang et al., 2010) on modern high-performance graphic processing units (GPUs) with the compute unified device architecture (CUDA) programming model. Within the framework of the meshless method, clouds of points used as basic computational stencils are distributed in the whole flow domain. The spatial derivatives of the governing equations are discretised by the moving-least square scheme on every cloud of points. Roe’s approximate Riemann solver is adopted to compute the convective flux. A dual-time stepping approach, which iterates in physical and pseudo temporal spaces, is employed to obtain the time-accurate solution. Simulation of steady compressible flows over a fixed aerofoil is firstly carried out to verify the GPU implementation of the method. Then it is extended to compute unsteady flows past oscillatory aerofoils. Numerical outcomes are compared with experimental and/or other reference results to validate the method. Significant performance speedup of more than an order of magnitude is verified by the numerical results. Systematic analysis shows that GPU is more energy efficient than CPU for solving aerodynamic problems. This demonstrates the potential of the proposed method to solve fluid–structure interaction problems

"Where iron is, there is the fatherland!" a note on the relation of privilege and monopoly to war,

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CatalogingThomas S. Hansen2010111