A novel numerical approach for the solution of two-dimensional viscous incompressible fluid flows

A new finite volume, Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm simulation of two-dimensional (2-D) incompressible viscous flow is developed. We solved the 2-D linearized Navier-Stokes equations in a sample cell analytically to obtain a velocity profile and used it in the numerical method. Fluid flow simulations were conducted inside a lid-driven square cavity, 2-D channel, and over a backward-facing step as benchmarks to assess the accuracy and speed of the present method. Comparisons are made mainly by Patankar’s numerical method and other experimental and numerical approaches depending on the case. By employing the provided 2-D velocity profile, the accuracy of the simulation is enhanced while reducing the computational time compared to Patankar's method. Conducting careful mesh refinement studies for the present and Patankar’s methods revealed that the present method can converge to the final solution using a coarser mesh. This capability results in a significant reduction in computational time, despite requiring computation of additional relations.