Implementation and analysis of a parallel multigrid method for Poisson equation in computational fluid dynamics

• Grant number: 16/21678-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2017
• End date: February 28, 2018
• Field of knowledge: Engineering - Mechanical Engineering - Transport Phenomena
• Principal Investigator: Leandro Franco de Souza
• Grantee: Luis Gustavo Lopes Costa
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims to implement and analyze the parallelization of multigrid method for Poisson equation solution, using for this domain decomposition in two directions. The algorithms with a better efficiency will be, in a second step, adopted for a code that solves Navier-Stokes equations for an incompressible two-dimensional flow of Newtonian fluid. The key point of the numerical solution of the Navier-Stokes equations for incompressible flows is the numerical solution of the Poisson equation. The study group has worked with parallelization study of this equation, but the current code uses domain decomposition only in one direction, so this project will allow a study aiming better performance. The results obtained from solutions of partial differential equations will be compared with analytical solution, in order to verify the accuracy of the methods implemented. The results of the parallel Navier-Stokes code for incompressible flow simulation will be compared with other results, to check the final code. Another objective is to verify the performance and code speed-up, comparing the total time spent in the sequential case (a single processor) and parallelized case (two or more processors). (AU)