A novel flux approximation scheme for spherically symmetric conservation laws

We apply the finite volume method to a spherically symmetric conservation law of advection-diffusion-reaction type. For the numerical flux we use the so-called complete flux scheme. In this scheme the flux is computed from a local boundary value problem for the complete equation, including the source term. As a result, the numerical flux is the sum of a homogeneous flux and an inhomogeneous flux. The resulting scheme has only a three-point stencil and is second order accurate, uniformly in the local Peclet numbers