Variable grid scheme applied to turbulent boundary layers

Theoretical Fluid Dynamics Division 5643, Sandia Laboratories, Albuquerque, New Mexico 87115, USA
Computer Methods in Applied Mechanics and Engineering (Impact Factor: 2.96). 09/1974; 4(2):179-194. DOI: 10.1016/0045-7825(74)90033-4


A Crank-Nicolson type finite-difference scheme with a nonuniform grid spacing has been interpreted in terms of a coordinate stretching approach to show that it is second-order accurate. The variable grid scheme is applied to a flat plate laminar to turbulent boundary layer flow with a rapidly changing grid interval across the layer. The accuracy of the solution is determined for a different number of intervals and compared to results obtained with the Keller box scheme. The influence of changing the grid spacing on the accuracy of the solutions is determined for one coordinate stretching or grid spacing relation. The use of Richardson extrapolation is also investigated.

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    • "If the mesh is uniform, the finite-difference scheme provides the second-order approximation with respect to both x and y. The two momentum equations are solved by the Blottner-type technique [11], which is well suited for marching problems. The induction equation is solved at each time step using the well-known ADI method. "
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    ABSTRACT: I0. I Introduction. This paper is a review of recent developments and problem areas in computational fluid dynamics, wherein "recent" is defined in relation to the publication of my book (Roache, 1972). (For brevity, that book will be referred to as "CFD" in this paper). Some of these topics were mentioned in CFD but not emphasized sufficiently; others were not in existence at the time of writing. CFD is not a truly comprehensive review of all the work done in the area up to mid-1972, and this review article is much less so for the work done up to the time of this writing, which is the fall of 1974. It is hoped that this review will still be of some utility, especially to younger people just getting into the field. 10.2 Significant General Publications. The literature in computational fluid dynamics has become very extensive, so that general, wide-ranging publications are very valuable. Three sets of conference proceedings are recommended: the AIAA Computational Fluid Dynamics Conference of July 1973 at Palm Springs (AIAA, 1973), and the Third (Paris) and Fourth (Boulder) International Conferences on Numerical Methods in Fluid Dynamics (Cabannes and Temann, 1972; Riehtmyer, 1974). These two biannual affairs alternate, so that we may expect another addition of a conference proceedings to the literature every year. In addition, three survey works are to be recommended. The AGARDograph by Taylor (1973) covers inviscid and viscous flows throughout the Mach number range from incompressible, transonic, through supersonic flows. It contains 261 references and covers well the background for "conventional" methods. The article by Orszag and Israeli (1974) in the Annual Review of Fluid Mechanics series is recommended for an introduction to higher-order methods and to spectral methods, and for general discussions on viscous flow simulation. The monograph by Kreiss and Oliger (1973) presents a detailed analysis of higher-order finite difference methods for inviscid equations, and will provide the nonmathematician with the background vocabulary for mathematical papers.
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