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Influence of the discretisation net on the accuracy of results in a diagnostic model for wind field adjustment

Brzozowska L.

Journal of Theoretical and Applied Computer Science

2013

Vol. 7, nr 2

31--44

Computational efficiency of model is a key factor which determines its practical application. The paper presents the algorithms which ensure the computational efficiency of a model of the air velocity field. The main step of modelling the air velocity field by means of the diagnostic model is the procedure of adjusting the initial field. The initial wind field is computed by interpolation of data from meteorological stations. The goal of adjusting the initial field is to ensure that the air velocity field satisfies the continuity equation in an area with a complex landform. The task is reduced to solving the Poisson equation. Finite difference methods with equidistant and non-equidistant nodes are applied. The discretisation net must be properly dense for a complex terrain. For an equidistant net this means that the computing time is extended and a numerical simulation might not be efficient. This problem can be reduced by using a non-equidistant mesh, in which the nodes near the places where we expect a significant change in the air velocity are condensed. In this paper the nonequidistant net is adapted for an example of terrain with an isolated hill. The hybrid approach is proposed in this work. The parabolic function for node distribution is used in the horizontal direction when in the vertical direction the Chebyshev nodes are applied. The results of the numerical analysis show the usefulness of a non-equidistant net in terms of accuracy and computational effectiveness.