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

A method of simulating behavior of a flow interacting with an object, the method providing a simulated numerical representation in N dimensions, N≧3, that is composed of a plurality of approximated values at a multitude of points in at least a part of space where the flow interacts with the 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 means of 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, the method comprising the steps of:

• using for the part of space a discrete N-dimensional grid constructed by N families of coordinate lines;
• computing, in at least one point P of the grid, called the point of computation, an approximated value DpA of Dp with an error εn, 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,
• choosing the computational functions for the approximated value DpA in such a way that the approximated value DpA is optimized for the preferential direction, and
• 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 Nf of the coordinate lines, the first coordinate line belonging to the family Nf is different from and not adjacent to the second coordinate line belonging to the same family Nf;
• and
• outputting the numerical representation that simulates, for the part of space, behavior of the flow interacting with the object.