Multigrid methods with applications to reservoir simulation

Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to obtain Moore-Penrose solutions of the singular systems encountered. For solving anisotropic equations, semicoarsening and line smoothing techniques are used with multiple coarse grid methods to improve convergence. Two-level convergence factors are estimated using multicolor. In the case where each operator has the same stencil on each grid point on one level, exact multilevel convergence factors can be obtained. For solving partial differential equations with discontinuous coefficients, interpolation and restriction operators should include information about the equation coefficients. Matrix-dependent interpolation and restriction operators based on the Schur complement can be used in nonsymmetric cases. A semicoarsening multigrid solver with these operators is used in UTCOMP, a 3-D, multiphase, multicomponent, compositional reservoir simulator. The numerical experiments are carried out on different computing systems. Results indicate that the multigrid methods are promising

Multigrid methods with applications to reservoir simulation

Multigrid methods are studied for solving elliptic partial differential equations. Focus is on parallel multigrid methods and their use for reservoir simulation. Multicolor Fourier analysis is used to analyze the behavior of standard multigrid methods for problems in one and two dimensions. Relation between multicolor and standard Fourier analysis is established. Multiple coarse grid methods for solving model problems in 1 and 2 dimensions are considered; at each coarse grid level we use more than one coarse grid to improve convergence. For a given Dirichlet problem, a related extended problem is first constructed; a purification procedure can be used to obtain Moore-Penrose solutions of the singular systems encountered. For solving anisotropic equations, semicoarsening and line smoothing techniques are used with multiple coarse grid methods to improve convergence. Two-level convergence factors are estimated using multicolor. In the case where each operator has the same stencil on each grid point on one level, exact multilevel convergence factors can be obtained. For solving partial differential equations with discontinuous coefficients, interpolation and restriction operators should include information about the equation coefficients. Matrix-dependent interpolation and restriction operators based on the Schur complement can be used in nonsymmetric cases. A semicoarsening multigrid solver with these operators is used in UTCOMP, a 3-D, multiphase, multicomponent, compositional reservoir simulator. The numerical experiments are carried out on different computing systems. Results indicate that the multigrid methods are promising

Modelling of Extreme Ocean Waves Using High Performance Computing

This thesis describes the development of a fully nonlinear numerical model for the simulation of surface water waves. The model has the ability to compute the evolution of both limiting and overturning waves arising from the focussing of wave components in realistic ocean spectra. To accomplish this task, a multiple-flux implementation of a boundary element method is used to describe the evolution of a free surface in the time domain over an arbitrary bed geometry. Unfortunately, boundary element methods are inherently computationally expensive and although approximations exist to reduce the complexity of the problem, the effects of their use in physical space is unclear. To overcome some of the computational intensity, the present work employs novel computational approaches to both reduce the run time of the simulations and make accessible predictions of wave fields that were previously unfeasible. The advances in computational aspects are made through the use of parallel algorithms running in a distributed computing environment. Further acceleration is gained by running parts of the algorithm on many-core co-processing devices in the form of the, habitually called, graphics processing unit. Once a reasonably efficient implementation of the boundary element method is achieved, attention is turned to further algorithmic optimisations, particularly in respect of computing the kinematics field underlying the extreme wave events. The flexibility of the model is demonstrated through the accurate simulation of extreme wave events, this includes near-breaking and overturning wave phenomena. Finally, by harnessing the power of high performance computing technologies, the model is applied to an engineering design problem concerning the wave-induced loading of an offshore jacket structure. The work presented is not merely a study of a single wave event and its interaction with a structure, but rather a whole multitude of wave-structure interaction events that could not have been computed within a realistic time frame were it not for the use of high performance computing. The outcome of this work is the harnessing of distributed and accelerated computing to enable the rapid calculation of numerous fully nonlinear wave loading events to provide a game changing outlook on structural design and the reliability for offshore structures; such calculations having not previously been possible

Aeronautical engineering: A continuing bibliography with indexes (supplement 296)

This bibliography lists 592 reports, articles, and other documents introduced into the NASA scientific and technical information system in Oct. 1993. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics