Solution of Burgers' equation for large Reynolds number using finite elements with moving nodes
Abstract
Accurate solutions to Burgers' equation are presented for a Reynolds number of 10,000, and the method of nodal movement is developed using a generalization of the algorithm of Caldwell et al. (1981). Using eight intervals (seven nodes) in the xdirection and a time interval k = 0.005, good agreement was found at t = 1 with the results of Mitchell and Griffiths (1980), with improved agreement for the case of 16 intervals (15 nodes). Results show how the nodes move towards the regions of steepest gradient and gradient change. Good agreement is also found between results at t = 0.5 for eight intervals (seven nodes) and the results of Christie et al. (1980), with improved agreement for 16 intervals (15 nodes).
 Publication:

Applied Mathematics Mechanics English Edition
 Pub Date:
 June 1987
 Bibcode:
 1987ApMaM..11..211C
 Keywords:

 Burger Equation;
 Computational Fluid Dynamics;
 Finite Element Method;
 Fluid Flow;
 Mathematical Models;
 Reynolds Number;
 Convective Flow;
 Differential Equations;
 Fluid Dynamics;
 RungeKutta Method;
 Fluid Mechanics and Heat Transfer