| This dissertation describes the details of the development of a general, stable and efficient computer code for simulating transient, three-dimensional fluid flows with properly chosen computational boundaries as well as physical boundaries. The topics in the description include: (1) the numerical techniques used in the computer code, which includes a refined version of an existing algorithm for solving the Navier-Stokes and the magnetohydrodynamic (MHD) equations, (2) extensive usage of a fast solver for linear systems of equations, (3) application of the method of characteristics to solving multi-dimensional MHD time-dependent boundary conditions, and (4) a series of numerical experiments to validate the numerical techniques and the computer coding. And finally, a simulation case is done on a shear motion induced phenomena in the solar corona that serves as an example application to demonstrate the usefulness of the computer code.; The algorithm developed in this study for solving the difference equations of the Navier-Stokes and MHD equations is called the Nimble Implicit Continuous-fluid Eulerian (NICE), algorithm which is a refined version of the FICE algorithm (Hu and Wu, Journal of Computational Physics 55 (1984), 33). The NICE algorithm is a pressure-based algorithm that solves the equations through a single-loop iteration in which the velocity field is solved within a predictor step and corrected by the corrector that results from a Poisson-type pressure correction equation which simultaneously satisfies the continuity equation, the momentum equation, and the equation of state. All of the formulated difference equations are expressed in linear systems of equations and solved by the solver that incorporates an incomplete pre-condition technique called the Dupont-Kendall-Rachford (DKR) partial factorization and the ORTHOMIN accelerator procedure in an iterative manner.; The time-dependent boundary conditions are formulated in such a way that through boundary treatments the characteristic method can apply to any kind of time-dependent boundary conditions for multi-dimensional MHD problems. Among them are the non-reflecting and coupled boundary conditions which are developed and applied in this study.; The numerical experiments to verify this code include a time-dependent compressible flow, a steady incompressible Hartmann flow, and a time-dependent plasma critical shear flow. In the numerical experiment for plasma critical shear flow, the results suggest a mechanism which could be used to explain the observed non-thermal line broadening in solar active regions during quiescent periods by a transition to MHD 'non-equilibrium' with the generation of MHD waves from the lower solar atmosphere. |
