Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization

A major difficulty in computing engineering Rows at high Reynolds number is the need for non-uniform grids adapted to solid boundaries that may be mov ing or changing shape. These non-uniform grids are expensive to calculate a nd cannot be used with the most accurate or efficient numerical schemes. We present one solution to this problem: a Brinkman (volume) penalization of the obstacle which allows an efficient pseudo-spectral method to he used to solve the Navier-Stokes equations on a Cartesian grid. Although this is th e most severe test of the penalization (due to the global support of the Fo urier basis), it is shown that the method still yields reasonable results. We also present an analytical solution of Stokes flow calculated using the penalization which illustrates the error and continuity properties of the a pproach. Work is currently underway to implement the penalization approach in a wavelet basis. (C) 2001 Editions scientifiques et medicales Elsevier S AS.