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U.S. Department of Energy
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Variable grid scheme for discontinuous grid spacing and derivatives

Conference ·
OSTI ID:6317559
In a previous paper, a Crank-Nicolson scheme with a variable grid was developed for solving turbulent boundary layer flows. It was demonstrated that this method is second-order accurate if the grid is specified with a smooth analytical expression; as the grid is refined according to this expression, the numerical error decreases as the square of the reciprocal of the number of mesh intervals employed. Although this approach is adequate for many problems, there are cases where a discontinuous change in mesh size is more convenient. In addition, there are problems where the derivative of the dependent variable is discontinuous and the previous Crank-Nicolson scheme is inappropriate. The discontinuous derivative can occur as the result of using different coordinate transformations for various regions of a flow problem. If the coefficients in the governing equations are discontinuous, the derivative of the dependent variable is also discontinuous. This type of problem occurs when a boundary layer flow of gas over a liquid layer is solved as one problem. This investigation was concerned with an extension of the Crank-Nicolson approach to cases where the grid spacing is arbitrary and discontinuous, and has resulted in a new Crank-Nicholson type finite difference scheme. The important conclusions about the method are: only certain second-order accurate relations for determining the wall velocity gradient should be used in evaluating the accuracy of the scheme; second-order behavior of this scheme can be retained on grids with discontinuous spacing; and the method developed can be readily applied to problems with discontinuous derivatives.
Research Organization:
Sandia Labs., Albuquerque, NM (USA)
DOE Contract Number:
EY-76-C-04-0789
OSTI ID:
6317559
Report Number(s):
SAND-79-0209C; CONF-790614-2
Country of Publication:
United States
Language:
English