Local grid refinement technique for problems with small circular internal boundaries

In this work we propose a local grid refinement method for solution of 2D problems with local circular sources of the small size which allows an accurate resolution of the source boundary. The resulting adaptive grid inherits local orthogonality and regularity properties of the standard Cartesian grids which makes possible an easy utilization of standard finite volume techniques (e.g., standard two-point flux approximation). Comparative studies performed on the Stefan test problem demonstated higher accuracy of the propsed algorithm in comparison with standard approximation using rectangular grids with the same number of computational cells.