The flux integral method for multidimensional convection and diffusion (Q1900564)

Based on the flux integral method, the authors present three techniques to estimate efficiently the multidimensional convective-plus-diffusive fluxes in a strictly conservative formulation, using an explicit forward-in-time, single-step update formula. The flux integral method yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudoflux-difference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation and on the given cell-averaged data. Three proposed schemes are briefly compared using the rotating Gaussian hill test problem under purely convective conditions.