EXAMPLES OF EXACT CONSTRUCTION OF GEOMETRICALLY OPTIMAL TWODIMENSIONAL GRIDS
A.F. Sidorov VANT. Ser.: Mat. Mod. Fiz. Proc 1994. Вып.4. С. 1822.
Classes of exact solutions were derived for EulerOstrogradsky’s equations, corresponding to nonlinear combined functional, with the help of which regular curvilinear grids, close to uniform and ortogonal ones are constructed. In general case, the above mentioned classes are described by the system of ordinary differential equations of the 8th order for which the problem of Cauchy is posed. In a specific symmetric case the system is reduced to one nonlinear equation of the 4th order, which has been integrated to the end in quadratures. The influence of the weight in terms of the functional responsible for orthoganality on quality of grids has been investigated. The results of numerical calculations are given. The constructed solutions may, for example, serve as tests for investigation of different numerical methods for grid generation.
