Browsing by Subject "Coupling methods"
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Item High Resolution Numerical Methods for Coupled Non-linear Multi-physics Simulations with Applications in Reactor Analysis(2011-10-21) Mahadevan, Vijay SubramaniamThe modeling of nuclear reactors involves the solution of a multi-physics problem with widely varying time and length scales. This translates mathematically to solving a system of coupled, non-linear, and stiff partial differential equations (PDEs). Multi-physics applications possess the added complexity that most of the solution fields participate in various physics components, potentially yielding spatial and/or temporal coupling errors. This dissertation deals with the verification aspects associated with such a multi-physics code, i.e., the substantiation that the mathematical description of the multi-physics equations are solved correctly (both in time and space). Conventional paradigms used in reactor analysis problems employed to couple various physics components are often non-iterative and can be inconsistent in their treatment of the non-linear terms. This leads to the usage of smaller time steps to maintain stability and accuracy requirements, thereby increasing the overall computational time for simulation. The inconsistencies of these weakly coupled solution methods can be overcome using tighter coupling strategies and yield a better approximation to the coupled non-linear operator, by resolving the dominant spatial and temporal scales involved in the multi-physics simulation. A multi-physics framework, KARMA (K(c)ode for Analysis of Reactor and other Multi-physics Applications), is presented. KARMA uses tight coupling strategies for various physical models based on a Matrix-free Nonlinear-Krylov (MFNK) framework in order to attain high-order spatio-temporal accuracy for all solution fields in amenable wall clock times, for various test problems. The framework also utilizes traditional loosely coupled methods as lower-order solvers, which serve as efficient preconditioners for the tightly coupled solution. Since the software platform employs both lower and higher-order coupling strategies, it can easily be used to test and evaluate different coupling strategies and numerical methods and to compare their efficiency for problems of interest. Multi-physics code verification efforts pertaining to reactor applications are described and associated numerical results obtained using the developed multi-physics framework are provided. The versatility of numerical methods used here for coupled problems and feasibility of general non-linear solvers with appropriate physics-based preconditioners in the KARMA framework offer significantly efficient techniques to solve multi-physics problems in reactor analysis.Item Linear solvers and coupling methods for compositional reservoir simulators(2010-12) Li, Wenjun, doctor of engineering; Sepehrnoori, Kamy, 1951-; Delshad, MojdehThree compositional reservoir simulators have been developed in the Department of Petroleum and Geosystems Engineering at The University of Texas at Austin (UT-Austin): UTCOMP (miscible gas flooding simulator), UTCHEM (chemical flooding simulator), and GPAS (General Purpose Adaptive Simulator). UTCOMP and UTCHEM simulators have been used by various oil companies for solving a variety of field problems. The efficiency and accuracy of each simulator becomes critically important when they are used to solve field problems. In this study, two well-developed solver packages, SAMG and HYPRE, along with existing solvers were compared. Our numerical results showed that SAMG can be an excellent solver for the usage in the three simulators for solving problems with a high accuracy requirement and long simulation times, and BoomerAMG in HYPRE package can also be a good solver for application in the UTCHEM simulator. In order to investigate the flexibility and the efficiency of a partitioned coupling method, the second part of this thesis presents a new implementation using a partition method for a thermal module in an equation-of-state (EOS) compositional simulator, the General Purpose Adaptive Simulator (GPAS) developed at The University of Texas at Austin. The finite difference method (FDM) was used for the solution of governing partial differential equations. Specifically, the new coupled implementation was based on the Schur complement method. For the partition method, two suitable acceleration techniques were constructed. One technique was the optimized choice of preconditioner for the Schur complement; the other was the optimized selection of tolerances for the two solution steps. To validate the implementation, we present simulation examples of hot water injection in an oil reservoir. The numerical comparison between the new implementation and the traditional, fully implicit method showed that the partition method is not only more flexible, but also faster than the classical, fully implicit method for the same test problems without sacrificing accuracy. In conclusion, the new implementation of the partition method is a more flexible and more efficient method for coupling a new module into an existing simulator than the classical, fully implicit method.The third part of this thesis presents another type of coupling method, iterative coupling methods, which has been implemented into GPAS with thermal module, FICM (Fully, Iterative Coupling Method) and GICM (General, Iterative Coupling Method), LICM (Loose, Iterative Coupling Method). The results show that LICM is divergent, and GICM and FICM can work normally. GICM is the fastest among the compared methods, and FICM has a similar efficiency as CFIM (Classic Fully Implicit Method). Although GICM is the fastest method, GICM is less accurate than FICM for in the test cases carried out in this study.