Semi-implicit method for pressure-linked equations (SIMPLE) ⇓ solution in MATLAB®

Abstract

This work presents a method for the solution of fundamental governing equations of computational fluid dynamics (CFD) using the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) in MATLAB®. The fundamental governing equations of fluid mechanics are based on three laws of conservation, referred to as the law of conservation of mass, the law of conservation of momentum and the law of conservation of energy. The continuity equation represents the law of conservation of mass, the Navier-Stokes equations represent the law of conservation of momentum, and the energy equation represents the law of conservation of energy. In SIMPLE, the continuity and Navier-Stokes equations are required to be discretized and solved in a semi-implicit way. This article presents the discretization and method of solution applied to the flow around a 2-D square body. Code is written in MATLAB®. The results show the pressure and velocity fields of the converged solution.