Simulation of two-phase flow processes in heterogeneous porous media with adaptive methods

In recent years the demand for numerical simulations which help to support the work of engineers has constantly gained weight. In the same way the computational power advances, the complexity of the problems and demands posed to the numerical simulation tools increases, too. This thesis expands the simulation tool MUFTE-UG for two-phase flow processes in porous media with adaptive methods. The approaches presented here can be divided into two parts: On the one hand, a space adaptive methods is introduced. Here, the element-size resolution throughout the discretization mesh is changed in certain areas from time step to time step. A marking of the relevant elements which need to be refined or coarsened is realized by an empirically derived error indicator. While at first three different indicators are compared, the final investigations of the various test cases are performed with an indicator locating a steep gradient of the saturation distribution in the system. As it shows that the applied h-adaptive strategy is not mass conservative due to mesh manipulations, an algorithm is developed which ensures the mass preservation for coarsening as well as for refinement. On the other hand, the discretization method is adaptively adjusted inside the domain. Since advection-dominated processes require an other numerical treatment than diffusion-dominated processes (in the here presented case realized by the application of a 'fully upwinding' or a 'centrally weighted' scheme), at first a suitable indicator needs to be found which accounts for these processes. For this, the two-phase (element) Peclet number is derived which describes the ratio between advection and diffusion. The developed methods are applied to homogeneous and heterogeneous test cases. For the choice of the homogeneous test cases it is considered that the here introduced methods need to be capable of handling purely advection-dominant problems (e.g. Buckley-Leverett problem), purely diffusion-dominant problems (e.g. McWhorter problem) and problems, where both effect appear in the domain at the same time (e.g. Sandbox problem). The heterogeneous test case resembles the Sandbox problem with a lense. Overall it can be said that the deployed space adaptive methods work very well for all the investigated test cases. The results obtained by the adaptive choice of discretization method are only mildly satisfactory. Here it shows, especially for the heterogeneous case, that the switch to the centrally weighted scheme needs a very careful adjusting. (orig.)Available from TIB Hannover: RA 1064(120) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman