The method of fundamental solutions for Brinkman flows. Part II. Interior domains

In part I, we considered the application of method fundamental solutions (MFS) for solving numerically Brinkman fluid flow in unbounded porous medium outside obstacles known or unknown shapes. this companion paper consider corresponding interior problem a bounded which contains an rigid inclusion $$D \subset \Omega $$ . The D is to be identified by pair Cauchy data represented velocity and traction on boundary $$\partial pressure incompressible viscous $$\Omega \backslash \overline{D}$$ are approximated linear combinations fundamentals system with sources (singularities) placed closure solution domain, i.e. \cup \big ({\mathbb {R}}^2\backslash \overline{\Omega } )$$ , assuming, simplicity, that analyse planar domains. By further assuming obstacle star-shaped (with respect origin), inverse recasts as minimization nonlinear Tikhonov’s regularization functional MFS expansion coefficients discretized polar radii defining D. This subject simple bounds variables solved using MATLAB optimization toolbox routine lsqnonlin.