Analysis and Application of a Stabilized Collocated Finite Volume Method for Stokes-Darcy Problems

Abstract

This thesis is devoted to finite volume solution of Stokes-Darcy type problems both in decoupled and coupled forms. Combining finite volume methodology and a stabilization procedure based respectively on collocation and pressure jumps control, novel finite volume schemes are developed and theoretically analyzed. Hence, stability and optimal convergence are achieved. Numerical results are presented for some standard test problems. These attest the remarkable computational performance of proposed schemes.