A toolkit for computational fluid dynamics using spectral element method in Scilab

Abstract

Computational Fluid Dynamics (CFD) is a discipline that solves a set of equations governing the fluid flow over any geometrical configuration. Three classes of solution techniques have emerged in CFD namely, the finite difference techniques, the finite element methods, and the spectral techniques. The spectral-element method combines the generality of the finite element method with accuracy of spectral techniques. This technique makes use of a Lobatto nodal base. One of the advantages of using spectral element method is that a stable solution algorithms and high accuracy can be achieved with a low number of elements under a broad range of conditions. In the present study spectral element method software library is developed and implemented using Scilab, which is a high-level, numerically oriented programming language an also an open source. In the present study the software library of Scilab has been used to develop a toolkit for one dimension steady diffusion equation, unsteady diffusion equation, and Laplace’s equation. The accuracy of the spectral method has also been emphasized by comparing it with the finite element method solution.