Time-dependent non-uniform grids for parabolic equations
A method based on a time dependent coordinate transformation has been applied to solve Burgers' equation. The numerical solution has been compared to the analytical solution of Lighthill . The numerical results agree completely with the analytical ones. They have been obtained with very large time steps because a fast implicit non-iterative algorithm has been employed for the time discretization. The number of grid points in the space discretization is very low because the coordinate transformation gives a steady shock in the “new” coordinate.
KeywordsGrid Point Coordinate Transformation Error Distribution Mesh Point Implicit Scheme
Unable to display preview. Download preview PDF.
- 1.M.J. Lighthill, “Surveys in Mechanics” (G.K. Batchelor and R.M. Davis, Eds.), p. 250, Academic Press, New Yrok & London, 1956.Google Scholar
- 4.P. Orlandi and J.H. Ferziger, AIAA J., 19 (1981), 1408.Google Scholar
- 5.W.R. Briley and H. McDonald, Lecture Notes in Physics, vol. 35, 105–110, Springer Verlag, New York, 1975.Google Scholar
- 6.R.M. Beam and R.F. Warming, AIAA J., 16 (1978), 393.Google Scholar
- 7.P. Orlandi, “Direct Simulation of Burgulence”, Proceedings of CTAC-83, J. Noye and C. Pletcher, North-Holland Publ. Company, p. 641, 1983.Google Scholar