The method of fundamental solutions for the Oseen steady-state viscous flow past obstacles of known or unknown shapes

Abstract

In this paper, the steady-state Oseen viscous flow equations past a known or unknown obstacle are solved numerically using the method of fundamental solutions (MFS), which is free of meshes, singularities, and numerical integrations. The direct problem is linear and well-posed, whereas the inverse problem is nonlinear and ill-posed. For the direct problem, the MFS computations of the fluid flow characteristics (velocity, pressure, drag, and lift coefficients) are in very good agreement with the previously published results obtained using other methods for the Oseen flow past circular and elliptic cylinders, as well as past two circular cylinders. In the inverse obstacle problem the boundary data and the internal measurement of the fluid velocity are minimized using the MATLAB© optimization toolbox lsqnonlin routine. Regularization was found necessary in the case the measured data are contaminated with noise. Numerical results show accurate and stable reconstructions of various star-shaped obstacles of circular, bean, or peanut cross-section.