A well balanced spectral volume model for constituents transport in one-dimensional flows

The treatment of advective fluxes in high-order finite volume models is well established, but this is not the case for diffusive fluxes, due to the conflict between the discontinuous representation of the solution and the continuous structure of analytic solutions. In this paper, a Derivative Reconstruction approach is proposed in the context of Spectral Volume methods, for the approximation of diffusive fluxes, aiming at the reconciliation of this conflict. The method is demonstrated by a number of numerical experiments, including the solution of Shallow-water Equations, complemented with the advective-diffusive transport equation of a conservative dissolved substance.