Numerical resolution of the incompressible Navier-Stokes equations: analysis of benchmark problems

Abstract

This thesis is aimed at solvingNavier-Stokes equation using Fractional Step Method also known as MAC method using staggered grids.Study was extended on deep study and researching about different schemes of higher order and how to improve the accuracy of solution to convection-diffusionequation by using high order schemes with and without flux limiters. Different schemes from literature has been described in this thesis. For comparison and validation of theory two different cases were tested Driven SMITH-HUTTON or Solenoidal flow problem and Diagonal flow problem for different mesh size are tested using own assembled MATLAB code.A separate code was prepared to model the Solution 2-dimensional solution to Incompressible Navier-Stokes Equations, by presenting a benchmark problem of LID-Driven Cavity.The most expensive task in the code is the solution to linear equations hence, solvers were used and discussed different solver to determine the most efficient one. Finite Volume Method has been implemented to study solution to this convection-diffusion equation