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Algorithms 2015, 8(2), 224-233; doi:10.3390/a8020224

Numerical Solution of Turbulence Problems by Solving Burgers’ Equation

Institute for Multidisciplinary Mathematics, Polytechnical University of Valencia, Camino de Vera, s/n, 46022 València, Spain
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Author to whom correspondence should be addressed.
Academic Editor: Francisco I. Chicharro
Received: 4 April 2015 / Revised: 27 April 2015 / Accepted: 30 April 2015 / Published: 8 May 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Abstract

In this work we generate the numerical solutions of Burgers’ equation by applying the Crank-Nicholson method and different schemes for solving nonlinear systems, instead of using Hopf-Cole transformation to reduce Burgers’ equation into the linear heat equation. The method is analyzed on two test problems in order to check its efficiency on different kinds of initial conditions. Numerical solutions as well as exact solutions for different values of viscosity are calculated, concluding that the numerical results are very close to the exact solution. View Full-Text
Keywords: Burgers’ equation; nonlinear system of equations; Newton’s scheme; high order iterative method Burgers’ equation; nonlinear system of equations; Newton’s scheme; high order iterative method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Cordero, A.; Franques, A.; Torregrosa, J.R. Numerical Solution of Turbulence Problems by Solving Burgers’ Equation. Algorithms 2015, 8, 224-233.

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