Numerical Solution of Turbulence Problems by Solving Burgers’ Equation

Algorithms

Alicia Cordero¹  Antonio Franques²  Juan R. Torregrosa² 

[1] Institute for Multidisciplinary Mathematics, Polytechnical University of Valencia, Camino de Vera, s/n, 46022 València, Spain;

关键词: Burgers’ equation;    nonlinear system of equations;    Newton’s scheme;    high order iterative method;   

DOI  :  10.3390/a8020224

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.