Abstracts

Novosibirsk participants

The paper gives an account of the geometrization of the comprehensive grid formulation proposed by the author in [1] and described in detail in [2]. It also presents an important generalization of the method [1] aimed at controlling the required grid properties. The paper applies some of the relations of the Riemannian geometry to obtaining new equations for generating grids with prescribed properties. Taking advantage of the relations established, the equations are converted into a compact form convenient for the numerical treatment by available algorithms. Studies of the behavior of the coordinate lines near boundary segments of the monitor surfaces and physical domains are carried out. Some relations of the mean curvatures of the monitor surfaces to the Beltramian equations for grid generation are exhibited. On the basis of an analysis of equations with boundary and interior layers [3] a form of the monitor functions for generating layer-resolving grids is established.

References

1. Liseikin V.D. On Generation of Regular Grids on n-Dimensional Surfaces, USSR Comput. Math. Math. Phys., 1991, Vol.31, №11, 47-57.
2. Liseikin V.D. Grid Generation Methods, Springer, Berlin, 1999.
3. Liseikin V.D. Layer-Resolving Grids and Transformations for Singular Perturbation Problems, VSP, Zest, 2001.

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