A numerical model based on the curvilinear coordinate system for the MAC method simplified
This work provides an incremental numerical approach for simulating fluid flows in complex geometries, relevant for computational fluid dynamics researchers.
The authors developed a numerical methodology using curvilinear coordinates and a simplified MAC method to simulate incompressible fluid flows without free surfaces, validating it on parallel plates, lid-driven cavity, and atherosclerosis problems with results matching literature.
In this paper we developed a numerical methodology to study some incompressible fluid flows without free surface, using the curvilinear coordinate system and whose edge geometry is constructed via parametrized spline. First, we discussed the representation of the Navier-Stokes and continuity equations on the curvilinear coordinate system, along with the auxiliary conditions. Then, we presented the numerical method -- a simplified version of MAC (\textit{Marker and Cell}) method -- along with the discretization of the governing equations, which is carried out using the finite differences method and the implementation of the FOU (\textit{First Order Upwind}) scheme. Finally, we applied the numerical methodology to the parallel plates problem, lid-driven cavity problem and atherosclerosis problem, and then we compare the results obtained with those presented in the literature. Keywords: finite differences, simplified MAC, curvilinear coordinates, parallel plates, did-driven cavity, atherosclerosis.