Remarks on Generation of the Orthogonal Structured Grids

S.I. Martynenko
2019 Herald of the Bauman Moscow State Technical University Series Natural Sciences  
Grid generation techniques have contributed significantly toward the application of mathematical modeling in large-scale engineering problems. The structured grids have the advantage that very robust and parallel computational algorithms have been proposed for solving (initial-)boundary value problems. Orthogonal grids make it possible to simplify an approximation of the differential equations and to increase computation accuracy. Opportunity of the orthogonal structured grid generation for
more » ... ing two- and three-dimensional (initial-)boundary value problems is analyzed in the article in assumption that isolines or isosurfaces of d (=2,3) functions form this grid. Condition of the isolines/isosurfaces orthogonality is used for formulation of the boundary value problems, the solutions of which will be form the orthogonal grid. A differential substitution is proposed to formulate the boundary value problems directly from the orthogonality condition of the grid. The substitution leads to the general partial differrential equations with undetermined coefficients. In the two-dimensional case, it is shown that the orthogonal grid generation is equivalent to the solution of partial differential equations of either elliptic or hyperbolic type. In three-dimensional domains, an orthogonal grid can be generated only in special cases. The obtained results are useful for mathematical modeling of the complex physicochemical processes in the technical devices
doi:10.18698/1812-3368-2019-1-16-26 fatcat:a2clo4iiujespbmnbl47fr2xum