Numerical grid generator in generalized coordinates

Abstract

The complexity of the fluid-dynamic problems make an analytical solution not possible in addition, an experimental solution may not be plausible in many contexts. The advancement of technology made numerical methods emerge as an alternative to these situations. One of the parameters that impact the solution of this method is the numerical grid used, which is still influenced by the geometry of the problem. In common coordinates systems, for complex geometries, numerical grids can generate a loss of accuracy in the solution of the problem. This work examines the possibility of implementing a mesh generator using elliptic partial differential equations to generate grids that fit the boundaries, even though they present complex geometries. After we developed and tested our generator with different boundaries, we evaluated the results, comparing their convergence as a function of mesh refinement made at layers in η direction. Accepting an error of 10−6, resulted, for 5 layers a mean of 65 iterations to converge, while for 25 layers were needed a mean of3487 iterations. Key-words: numerical grid, Computational fluid dynamics, complex geometries