Using Python to Solve the Navier-Stokes Equations-Applications in the Preconditioned Iterative Methods
Jia Liu *
Department of Mathematics and Statistics, University of West Flroida, Pensacola, Florida, 32514, USA.
Lina Wu
Department of Mathematics, Borough of Manhattan Community College, The City University of New York, New York, NY 10007, USA.
Xingang Fang
Department of Computer Science, University of West Flroida, Pensacola, Florida, 32514, USA.
*Author to whom correspondence should be addressed.
Abstract
This article describes a new numerical solver for the Navier-Stokes equations. The proposed solver is written in Python which is a newly developed language. The Python packages are built to solve the Navier-Stokes equations with existing libraries. We have created discretized coefficient matrices from systems of the Navier-Stokes equations by the finite difference method. In addition we focus on the preconditioned Krylov subspace iterative methods in the linearized systems. Numerical results of performances for the Preconditioned iterative methods are demonstrated. The comparison between Python and Matlab is discussed at the end of the paper.
Keywords: Python, Navier-Stokes equations, Iterative methods, Preconditioner.