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Title: | Numerical solutions of the burgers’ system in two dimensions under varied initial and boundary conditions |
Authors: | Kweyu, M. C. Manyonge, W. A. Koross, A. Ssemaganda, V. |
Keywords: | Hopf-Cole transformation Finite difference methods Analytic solution Crank-Nicolson scheme Explicit scheme |
Issue Date: | 2012 |
Publisher: | Chepkoilel University College |
Abstract: | In this paper, we generate varied sets of exact initial and Dirichlet boundary conditions for the 2-D Burgers’ equations from general ana- lytical solutions via Hopf-Cole transformation and separation of vari- ables. These conditions are then used for the numerical solutions of this equation using finite difference methods (FDMs) and in particular the Crank-Nicolson (C-N) and the explicit schemes. The effects of the variation in the Reynolds number are investigated and the accuracy of these schemes is determined by the L 1 error. The results of the explicit scheme are found to compare well with those of the C-N scheme for a wide range of parameter values. The variation in the values of the Reynolds number does not adversely affect the numerical solutions. |
URI: | http://ir.mu.ac.ke:8080/jspui/handle/123456789/5027 |
Appears in Collections: | School of Biological and Physical Sciences |
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