Aliasing formation and anti-aliasing filtering in spectral methods

• Grant number: 12/19161-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2013
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Leandro Franco de Souza
• Grantee: João Henrique Ribeiro Dainezi
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In many simulations of fluid flow can be admitted periodicity in one or more directions. One way to discretize the terms this (s) direction (s) is through the use of spectral methods. The use of spectral methods using Fourier transform ensures that the derivatives are calculated accurately, disregarding the rounding errors. The present work aims to study spectral methods (Fourier transforms) and check the generation of the effect of aliasing convolution products, and then consider ways to eliminate this effect. Initially, it will be discussed the Fourier transform methods and fast Fourier transform. In a second step, we discuss the convolution products. These products should be made in the physical space to minimize computational time. This product is generated aliasing effects that are undesirable in any numerical simulation involving convolution products. Finally should be studied methods of removing the aliasing effect, aiming to convolution products that have minimal influence on the results. The results obtained are compared with the analytical results for scan methods of anti-aliasing and the computational time required in each method.(AU)