Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes
Alexys Bruno‐Alfonso, Luben Cabezas‐Gómez, Hélio Aparecido Navarro · Scientific Electronic Library Online (São Paulo Research Foundation, Latin American and Caribbean Center on Health Sciences Information, Conselho Nacional de Desenvolvimento Científico e Tecnológico) · 2012
Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in partial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coordinates by setting up complementary equations. Such equations are obtained by either integral or smoothness conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.