Theses and Dissertations from UMD
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Item Fast Solvers and Preconditioners for Multiphase Flow in Porous Media(2018) Bui, Quan Minh; Elman, Howard; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Multiphase flow is a critical process in a wide range of applications, including carbon sequestration, contaminant remediation, and groundwater management. Typically, this pro- cess is modeled by a nonlinear system of partial differential equations derived by considering the mass conservation of each phase (e.g., oil, water), along with constitutive laws for the relationship of phase velocity to phase pressure. The problem becomes much more complex if the phases are allowed to contain multiple chemical species (also called components), as miscibility and phase transition effects need to be taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as phase pressure and phase saturation, i.e. they become ill-defined when a phase appears or dis- appears. Recently, a new approach for handling phase transition has been developed by formulating the system as a nonlinear complementarity problem (NCP). Unlike the widely used primary variable switching method (PVS), which requires a drastic reduction of the time step size when a phase appears or disappears, this approach is more robust and allows for larger time steps. One way to solve an NCP system is to reformulate the inequality constraints for the primary variables as a non-smooth equation using a complementary function (C-function). Because of the non-smoothness of the constraint equations, a semi-smooth Newton method needs to be developed. Another feature of the NCP approach is that the set of primary variables in this approach is fixed even when there is phase transition. Not only does this improve the robustness of the nonlinear solver, it opens up the possibility to use multigrid methods to solve the resulting linear system. The disadvantage of the complementarity approach, however, is that when a phase disappears, the linear system has the structure of a saddle point problem and becomes indefinite, and current algebraic multigrid (AMG) algorithms cannot be applied directly. In this work, we aim to address computational issues related to modeling multiphase flow in porous media. First, we develop and study efficient solution algorithms for solving the algebraic systems of equations derived from a fully coupled and time-implicit treatment of models of incompressible two-phase flow. We explore the performance of several precon- ditioners based on algebraic multigrid (AMG) for solving the linearized problem, including “black-box” AMG applied directly to the system, a new version of constrained pressure residual multigrid (CPR-AMG) preconditioning, and a new preconditioner derived using an approximate Schur complement arising from the block factorization of the Jacobian. We show that the new methods are the most robust with respect to problem character as de- termined by varying effects of capillary pressures, and we show that the block factorization preconditioner is both efficient and scales optimally with problem size. We then generalize the block factorization method and incorporate it into a multigrid framework which is based on the multigrid reduction technique to deal with linear systems resulting from the NCP approach for modeling compositional multiphase flow with phase transitions. We demon- strate the effectiveness and scalability of the method through numerical results for a case of two-phase, two-component flow with phase appearance/disappearance. Finally, we propose a new semi-smooth Newton method which employs a smooth version of the Fischer-Burmeister function as the C-function and evaluate its performance against the semi-smooth Newton method for two C-functions: the minimum and the Fischer-Burmeister functions. We show that the new method is robust and efficient for standard benchmark problems as well as for realistic examples with highly heterogeneous media such as the SPE10 benchmark.Item Quad Tilt Rotor Simulations in Helicopter Mode using Computational Fluid Dynamics(2005-12-05) Gupta, Vinit; Baeder, James D.; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The flow field around a simplified Quad Tilt Rotor (QTR) vehicle is simulated using computational fluid dynamics (CFD) for various low speed flight conditions in helicopter mode. A time-averaged rotor model is utilized, where the velocity field computed by CFD is coupled to blade element theory and a trim model to provide an equivalent time-averaged body force term in the compressible Navier-Stokes equations, instead of moving overset meshes; reducing the computational time while capturing the essential physics. Overset meshes are used to model the complicated geometry of the simplified aircraft fuselage and wings in order to ensure good resolution of viscous effects. The solution of the compressible Navier-Stokes equations are suitably modified using low Mach number preconditioning to properly scale the dissipation and enhance convergence. This approach is validated for the current work by comparison with experimental data for the downwash velocity underneath an isolated tilt rotor system as well as for the pressure distribution resulting on the surface of a single wing placed underneath such a tilt rotor system. A total of 8 grids with approximately 5.2 million grid points is then employed to simulate half of a simplified QTR geometry for a range of flight conditions. A high download (9% of thrust) is obtained in hover, as expected, when the QTR operates Out of Ground Effect (OGE), primarily from a strong download on the front and rear wings. A detailed analysis of the calculated flow field, along with chordwise pressure distributions and spanwise loadings on the wings, is performed to explain the observed decay in download on the vehicle with an increase in the forward flight speed. The high download obtained OGE in hover, becomes a strong upload (9% of thrust) when the vehicle operates In Ground Effect (IGE) with the wheels placed on the ground; primarily from a strong upload on the fuselage and inner portion of the rear wing. Upload observed IGE in hover gradually fades away with an increases in forward flight. An increase in forward flight speed eventually results in the flow along the ground unable to travel far upstream; the simulation shows the expected horseshoe shape of the wake near the ground. The simulations suggest that the uploads obtained IGE persist for high enough forward flight speed such that a significant increase in payload should be feasible for rolling takeoffs.