Applying hybrid methods to reduce nonphysical cycles in the flux field

Abstract

In this thesis we present the theoretical background for the two-point flux-approximation method; (TPFA), mimetic discretisation methods, and the multipoint flux approximation method; (MPFA). Theoretical arguments concerning monotonicity and the fact that loss of monotonicity may lead to oscillations and nonphysical cycles in the flux field are also discussed. TPFA is only consistent for $mathbf{K}$-orthogonal grids. Multipoint flux approximation methods and mimetic discretisation methods are consistent, even for grids that are not K-orthogonal, but sometimes they lead to solutions containing cycles in the flux field. These cycles may cause problems for some transport solvers and diminish the efficiency of others, and to try to cure this problem, we present two hybrid methods. The first is a hybrid mimetic method applying TPFA in the vertical direction and mimetic discretisation in the plane. The second hybrid method is the hybrid MPFA method applying TPFA in the vertical direction and MPFA in the plane. We present results comparing the accuracy of the methods and the number of cycles obtained by the different methods. The results obtained shows that the hybrid methods are more accurate than TPFA, and for specific cases they have less cycles than the original full methods.