Interpolation methods using radial function kernels in non-orthogonal grids

Resumo

In fluid dynamics, the numerical solution of time-dependent partial differential equations the values for
the dependent variables are calculated at discrete points. When the grid used is structured and orthogonal, there
are well-established methodology to perform the interpolation of the variable for any point of interest that does

not coincide with the points of the grid. This is not simple when it comes to a grid that is unstructured and non-
orthogonal. Non-orthogonality introduces a greater number of unknowns than equations, in this case it is necessary

to balance the number of unknowns with the number of equations and interpolate the information for the remainder
points that will be grouped as source terms. In this work, several bases of radial functions of global and compact
support interpolation were tested in orthogonal and non-orthogonal grids. The numerical results were compared
with those obtained by analytical solution and good agreement was found. Results are organized in terms of
precision and the computational effort required.