variavel0=<b>Márcio Ricardo Pivello</b> - pivello@mecanica.ufu.br Universidade Federal de Uberlândia
<b>Carlos Roberto Ribeiro</b> - cribeiro@mecanica.ufu.br Universidade Federal de Uberlândia
<b>Abstract.</b> In this work we present a scheme for smoothing 2D block-structured grids, which are widely used to solve CFD problems. Since these problems are often solved via finite volume method, the grid transition between adjacent blocks is of great importance in the convergence process. A multiblock grid is generated in two steps, namely the domain partition into quadrilateral subdomains, which are called blocks, and the structured grid generation within each block. The block generation in this work is manual and an initial structured grid is assumed to be given within each block. In order to obtain good results after solving the physical problem, some conditions concerning the grid must be observed: grid points located on a boundary shared by two blocks must have the same coordinates for each of them. Also, since this grid will be used later to solve CFD problems via finite volume methods, C2 continuity on the interface is important. To achieve such a smoothness we will use a Laplacian operator formulated in curvilinear coordinates. In order to ensure C2 continuity between adjacent blocks, the nodes located on the boundaries shared by two blocks are treated as if they were inside the block domain, that is: the Laplacian operator is applied to the boundary nodes, which become the last row / column of the block, and the new boundary nodes will be the ones located at the first row / column of the adjacent block, which will be the boundary conditions to the Laplacian operator. The smoothing process replaces the boundary nodes in order to obtain geometrically regular elements, and the design variables are the boundary nodes coordinates. These work as Dirichlet boundary conditions to the Laplacian operator, which will replace the internal nodes. The domain representation was done with parametric cubic splines, which were used to apply the boundary conditions too. The results show that the merging of the grid and block topology smoothing processes leads to good results and makes the algorithm implementation easier.
<b>Keywords.</b> Multiblock grids, grid smoothing, Laplacian operator, 2D grids.