Fourth-order method for solving the Navier-Stokes equations in a constricting channel
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Data
1997-11-30
Autores
Mancera, P. F. D. A. [UNESP]
Hunt, R.
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Resumo
A fourth-order numerical method for solving the Navier-Stokes equations in streamfunction/vorticity formulation on a two-dimensional non-uniform orthogonal grid has been tested on the fluid flow in a constricted symmetric channel. The family of grids is generated algebraically using a conformal transformation followed by a non-uniform stretching of the mesh cells in which the shape of the channel boundary can vary from a smooth constriction to one which one possesses a very sharp but smooth corner. The generality of the grids allows the use of long channels upstream and downstream as well as having a refined grid near the sharp corner. Derivatives in the governing equations are replaced by fourth-order central differences and the vorticity is eliminated, either before or after the discretization, to form a wide difference molecule for the streamfunction. Extra boundary conditions, necessary for wide-molecule methods, are supplied by a procedure proposed by Henshaw et al. The ensuing set of non-linear equations is solved using Newton iteration. Results have been obtained for Reynolds numbers up to 250 for three constrictions, the first being smooth, the second having a moderately sharp corner and the third with a very sharp corner. Estimates of the error incurred show that the results are very accurate and substantially better than those of the corresponding second-order method. The observed order of the method has been shown to be close to four, demonstrating that the method is genuinely fourth-order. © 1977 John Wiley & Sons, Ltd.
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Fourth-order methods, Navier-Stokes equations, Boundary conditions, Channel flow, Error analysis, Iterative methods, Navier Stokes equations, Nonlinear equations, Problem solving, Reynolds number, Vortex flow, Fourth order method, Newton iteration, Computational fluid dynamics, channel, fluid flow, vorticity, channel flow, fourth-order methods
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International Journal for Numerical Methods in Fluids, v. 25, n. 10, p. 1119-1135, 1997.