A simple projection method for the coupled Navier-Stokes and Darcy flows

Abstract

The flow through both an incompressible fluid region and a porous medium occurs in a wide range of applications encompassing industrial processes and geological phenomena. Recently, the fluid transport phenomena across the interface between the distinct regions have received increasing attention both from the mathematical and the numerical points of view. The primary objective of the present study lies in the development of a simple and efficient method for the computations of coupled Navier-Stokes and Darcy flows with complex interface conditions. A finite difference projection method is developed within a staggered grid framework to solve the coupled system in a segregated manner using primitive variables. Numerical simulations are carried out to demonstrate the order of convergence and its capability. The proposed method renders the versatility in solving the coupled system, and it is readily extendible to multi-physics fluid flows and turbulent flows for a broad range of applications.