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Method for the numerical simulation of a physical phenomenon with a preferential direction

  • US 7,239,990 B2
  • Filed: 02/18/2004
  • Issued: 07/03/2007
  • Est. Priority Date: 02/20/2003
  • Status: Active Grant
First Claim
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1. A computation method for simulating behavior of a flow interacting with an object, comprising the steps of:

  • developing a simulated numerical representation in N dimensions, N≧

    3, composed of a plurality of approximated values at a multitude of points in at least a part of space where a flow interacts with an object, the approximated values being of a physical parameter u of the flow to which is associated a velocity field {right arrow over (a)} which determines a preferential direction by executing a numerical scheme wherein at least one spatial pth derivative Dp, p≧

    1, of the parameter u is approximated at the points of the part of space, through the steps ofi) constructing a discrete N-dimensional grid constructed by N families of coordinate lines and using the constructed grid for the part of space,ii) computing, in at least one point P of the grid, called the point of computation, an approximated value of DpA of Dp with an error ε

    n, by using values uS of the parameter in a collection of grid points, called the stencil S, and computational functions, evaluated with the values uS, the computational functions depending on the numerical framework in which Dp is expressed, andiii) choosing the computational functions for the approximated value DpA in such a way that the approximated value DpA is optimized for the preferential direction,wherein the stencil S contains at least one point situated outside all the coordinate lines passing through the point of computation P, and the stencil S contains at least a first point and a second point, the first point being defined by N first coordinate lines of the N families of lines, the second point being defined by N second coordinate lines of the N families of lines, and for at least one family Nƒ

    of the coordinate lines, the first coordinate line belonging to the family Nƒ

    is different from and not adjacent to the second coordinate line belonging to the same family Nƒ

    ;

    outputting the simulated numerical representation that simulates, for the part of space, the behavior of the flow interacting with the object; and

    determining the behavior of the flow interacting with the object by using the output simulated numerical representation.

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