| Many flow problems in engineering and technology are coupled in their nature. Plenty of turbulent flows are solved by legacy codes or by ones written by a team of programmers with great complexity. As knowledge of turbulent flows expands and new models are introduced, implementation of modern approaches in legacy codes and increasing their accuracy are of great concern. On the other hand, industrial flow models normally involve multi-physical process or multi-domains. Given the different nature of the physical processes of each subproblem, they may require different meshes, time steps and methods. There is a natural desire to uncouple and solve such systems by solving each subphysics problem, to reduce the technical complexity and allow the use of optimized legacy sub-problems' codes. The objective of this work is the development, analysis and validation of new modular, uncoupling algorithms for some coupled flow models, addressing both of the above problems. Particularly, this thesis studies: i) explicitly uncoupling algorithm for implementation of variational multiscale approach in legacy turbulence codes, ii) partitioned time stepping methods for magnetohydrodynamics flows, and iii) partitioned time stepping methods for groundwater-surface water flows. For each direction, we give comprehensive analysis of stability and derive optimal error estimates of our proposed methods. We discuss the advantages and limitations of uncoupling methods compared with monolithic methods, where the globally coupled problems are assembled and solved in one step. Numerical experiments are performed to verify the theoretical results. |
