Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes

Abstract

Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian\ud determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in par-tial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coor-dinates by setting up complementary equations. Such equations are obtained by either integral or smoothness\ud conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.CNPqFAPES