200 1997 Erik Sterner erik@tdb.uu.se Finite Volume Discretizations of Convection-Diffusion Equations at Polar Mesh Singularities
Abstract
Structured meshes in computational fluid dynamics sometimes have polar
singularities. Here we study the accuracy of a finite volume
discretization applied to a scalar convection-diffusion equation using
such a mesh. Estimates of the global error and the truncation error
are derived in the max norm and the discrete
\(L_2\) norm. A multigrid accelerated explicit Runge--Kutta scheme is
used for bringing the semi-discrete system to a steady state, and the
convergence rate obtained on a polar mesh is
compared with the convergence rate on a quadratic mesh.