Solving the depth-averaged advection-diffusion equation on curvilinear grids using a hybrid flux-corrected transport technique

摘要

A numerical scheme has been developed to solve the depth-averaged advection-diffusion equation on non-orthogonal boundary-fitted curvilinear grids. The use of a finite-volume approach allows the diffusive terms to be solved using central-differences but the problem still remains of how to treat the advective terms in an Eulerian context. This problem is solved by the use of a characteristic based scheme which allows accurate calculation of fluxes through high-order interpolation functions. The fluxes are then limited using a flux-correction technique to give a scheme which maintains both conservation and monotonicity in the solution. The results show that the technique is accurate, conservative, monotonic and phase preserving.