Embedded finite volume technique for fluid/rigid-body interaction problems

Abstract

This work describes a formulation for the treatment of submerged rigid solids within the framework of the finite volume method. The proposal consists in considering the solid as a porous region and the hydrodynamic forces that arise from the Darcy terms. The methodology is implemented in an open code that allows largescale calculations. In the present work, we present the methodology and its verification using cases of study, to demonstrate spatio-temporal numerical convergence and the accuracy of the imposition of boundary conditions. For this purpose, cases that have an analytical solution are analyzed, such as the Pouiseuille flow, the first and second Stokes problems, and immersed walls that move with imposed movement generating different pressures between both faces. A moving cylinder analysis is shown to validate the numerical technique in comparison with cases reported in the literature. The analysis leads to stability conditions against external parameters such as permeability. The ability of the method to represent moving walls and immersed bodies with imposed movement is established.