Mancera, P. F. D. A. [UNESP]Hunt, R.2014-05-272014-05-271997-11-30International Journal for Numerical Methods in Fluids, v. 25, n. 10, p. 1119-1135, 1997.0271-2091http://hdl.handle.net/11449/65232A 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.1119-1135engFourth-order methodsNavier-Stokes equationsBoundary conditionsChannel flowError analysisIterative methodsNavier Stokes equationsNonlinear equationsProblem solvingReynolds numberVortex flowFourth order methodNewton iterationComputational fluid dynamicschannelfluid flowvorticitychannel flowfourth-order methodsArtigo10.1002/(SICI)1097-0363(19971130)25:10<1119::AID-FLD610>3.0.CO;2-4Acesso restrito2-s2.0-003127756282322894121087230000-0002-2080-8053