Advances in grid generation by Olga V. Ushakova

By Olga V. Ushakova

Grid new release offers with using grids (meshes) within the numerical answer of partial differential equations by means of finite components, finite quantity, finite modifications and boundary components. Grid new release is utilized within the aerospace, mechanical engineering and medical computing fields. This booklet provides new study within the box.

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However, for the considered problem, implementation of computations on the block grid involves serious difficulties. Indeed, the number of boundary nodes inside a tongue must increase with extending the tongue extends. For this reason, the grid line that separates the blocks cannot pass through the same boundary node during the compu­ tation. This leads to the necessity of designing an algorithm for periodically changing the structure of the blocks. This algorithm involves cumbersome remap procedures between grids of different structures.

6, 1 64 ( 1 987). 32, No. R An Elliptic Barrier-Type Grid Generator ... , Compound difference schemes for time-dependent equations on non-uniform nets, Communs. Numer. Methods in Engineering 10, No 2, 93 ( 1 994). , Almost conservative difference schemes for the equations of gas dynamics, Comput. Math. Math. Phys. 33, No. 1 1 , 1 68 1 ( 1 993). , On algorithms for computing the Riemann problem by means of Godunov's scheme, Comput. Math. Math. Phys. 40, No. 5, 746 (2000). , Towards the altimate conservative difference scheme.

3 New Grid Generator {x, Here we use the symbol fi ,j = Y)i ,j for notational brevity, and the formulas are written in the vector notation. The simplest way to construct the grid ( 1 . 1 ) is as follows (see [3]). Consider a family of lines, for definiteness, those corresponding to fixed values of the index j. The lines of this family are taken to be straight lines, with grid nodes distributed along them in some reasonable way. First, the quantities s� in the boundary j = 0 are computed: sg = 0, S�+1 = sY + I fi+1,o - fi,o I , i = 1 , .

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