FLUID FLOW MODELING WITH FREE SURFACE

Abstract

This study discussed modelling fluid flow with a free surface and a submerged obstacle in the fluid flow. To build the mathematical model, we assumed the fluid is incompressible, steady-state, and irrotational. Firstly, we used Newton’s second law, the law of mass conservation and the law of conservation of momentum to obtain the general Navier-Stokes equation. Then, the Euler-free surface equation and the Bernoulli equation were designed before making a free surface representation and linearizing the wave equation to obtain a fluid flow model. The resulting mathematical model is a Laplace equation with boundary conditions in the fluid.