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Fourth-order method for solving the Navier-Stokes equations in a constricting channel
  • Strathclyde University
  • Universidade Estadual Paulista (UNESP)
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.
Issue Date: 
International Journal for Numerical Methods in Fluids, v. 25, n. 10, p. 1119-1135, 1997.
Time Duration: 
  • 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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Appears in Collections:Artigos, TCCs, Teses e Dissertações da Unesp

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