The method of fundamental solutions for Brinkman flows. Part I. Exterior domains

The method of fundamental solutions (MFS) is developed for solving numerically the Brinkman flow in porous medium outside obstacles known or unknown shapes. MFS uses solution equation as boundary element (BEM), but single-layer representation desingularized by moving sources to fictitious points domain. In case unbounded past obstacles, these source are placed domain inside obstacle on a contracted pseudo-boundary. When known, then fluid media problem direct, linear and well-posed. an infinitely long circular cylinder, numerical found be very good agreement with available analytical solution. However, when has determined from velocity measurements at some fluid, resulting becomes inverse, nonlinear ill-posed. $$\hbox {MATLAB}^{\copyright }$$ optimization toolbox routine lsqnonlin employed minimizing least-squares gap between computed measured which further penalized extra smoothness regularization terms order overcome instability For proper choices parameters involved, accurate stable reconstructions achieved various star-shaped obstacles.