In order to understand tidal circulation and oceanic current for the seas around Taiwan, this study use a baroclinic unstructured grid model to build a high resolution model. This model use semi-implicit method to solve the dynamic of ocean movement and larger time step can be used to calculate. Unstructured grid can be used to resolve complex coastline and variation of depth. TaiDBMv6 depth data were chosen to describe the depth distribution and grid mesh size were determined by local depth, minimum mesh size is about 0.75 minutes, and maximum 13 minutes. Tidal boundaries use 8 constituents derived from FES2004 and calibrated with 34 tide station records. Data of 2009 were used to evaluate the model results. The average of all station root mean square error was 10.1 cm. Station at east side of Taiwan have smaller errors, which almost lower than 5 cm. The maximum error can be found inside Taiwan Strait, about 25cm, mainly caused by lack of depth data near the coastal area. For oceanic current model, GFS and NFS-MC CWB wind forecast were used as meteorology input. Initial fields and boundary condition are derived from HYCOM results. Nudging of salinity and temperature also were used to stabilize the model. Transport of Kuroshio of 2009 is about 17.0¡Ó3.2Sv. Maximum value is about 28.6Sv, occurred in summer. Minimum value is about 8.3Sv, occurred in winter.

The thesis presents work across three different subjects of investigations into the modelling of spray development and its interaction with non-reactive and reactive flow. The first part of this research is aimed to create a new and robust family of convective scheme to capture the interface between the dispersed and the carrier phases without the need to build up the interface boundary. The selection of Weighted Average Flux (WAF) scheme is due to this scheme being designed to deal with random flux scheme which is second-order accurate in space and time. The convective flux in each cell face utilizes the WAF scheme blended with Switching Technique for Advection and Capturing of Surfaces (STACS) scheme for high resolution flux limiters. However in the next step, the high resolution scheme is blended with the scheme to provide the sharpness and boundedness of the interface by using switching strategy. The proposed scheme is tested on capturing the spray edges in modelling hollow cone type sprays without need to reconstruct two-phase interface. A test comparison between TVD scheme and WAF scheme using the same flux limiter on convective flow on hollow cone spray is presented. Results show that the WAF scheme gives better prediction than the TVD scheme. The only way to check the accuracy of the presented models are evaluations according to physical droplets behaviour and its interaction with air. In the second part, due to the effect of evaporation the temperature profile in the released fuel vapour has been proposed. The underlying equation utilizes transported vapour mass fraction. It can be used along with the solution of heat transfer inside a sphere. After applying boundary conditions, the equation can provide a solution of existing conditions at liquid-gas interface undergoing evaporation and it is put in a form similar to well-known one-third rule equation. The resulting equation is quadratic type that gives an accurate prediction for the thermo-physical properties due to the non-linear relation between measured properties and temperature. Comparisons are made with one-third rule where both equations are implemented in simulating hollow cone spray under evaporation conditions. The results show the presumed equation performs better than one-third rule in all comparisons. The third part of this research is about a conceptual model for turbulent spray combustion for two combustion regimes that has been proposed and tested for n-heptane solid cone spray type injected into a high-pressure, high-temperature open reactor by comparing to the available experimental data and to results obtained using two well known combustion models named the Combined Combustion Model (CCM) and the unsteady two-dimensional conditional moment closure (CMC) model. A single-zone intermittent beta-two equation turbulent model is suggested to characterise the Lumped zone. This model can handle both unburned and burned zones. Intermittency theory is used to account for the spatially non-uniform distribution of viscous dissipation. The model suggests that the Lumped zone can be identified by using the concept of Tennekes and Kuo-Corrsion of isotropic turbulence that suggests that dissipative eddies are most probably formed as vortex tubes with a diameter of the order of Kolmogorov length scale and a space of the order of Taylor length scale. Due to the complexity of mixture motion in the combustion chamber, there exist coherent turbulent small scale structures containing highly dissipative vortices. The small size eddies play an important role in extinguishing a diffusion spray flame and have an effect on the combustion reaction at molecular scale because small scales turbulence increase heat transfer due to the dissipation. A common hypothesis in constructing part of the model is if the Kolmogorov length scale is larger than the turbulent flame thickness. The Lumped strategy benefits from capturing small reactive scales information provided by numerics to improve the modelling and understand the exact implementation of the underlying chemical hypothesis. The Lumped rate is estimated from the ratio of the turbulent diffusion to reaction flame thickness. Three different initial gas temperature test cases are implemented in simulations. Lumped spray combustion model shows a very good agreement with available experimental data concerning auto-ignition delay points.

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The development and numerical implementation of a three-dimensional Particle-In-Cell (PIC) methodology on unstructured Voronoi-Delauney tetrahedral grids is presented. Charge assignment and field interpolation weighting schemes of zero- and first-order are formulated based on the theory of long-range constraints for three-dimensional unstructured grids. The algorithms for particle motion, particle tracing, particle injection, and loading are discussed. Solution to Poisson's equation is based on a finite-volume formulation that takes advantage of the Voronoi-Delauney dual. The PIC methodology and code are validated by application to the problem of current collection by cylindrical Langmuir probes in stationary and moving collisionless plasmas. Numerical results are compared favorably with previous numerical and analytical solutions for a wide range of probe radius to Debye length ratios, probe potentials, and electron to ion temperature ratios. A methodology for evaluation of the heating, slowing-down and deflection times in 3D PIC simulations is presented. An extensive parametric evaluation is performed and the effects of the number of computational particles per cell, the ratio of cell-edge to Debye length, and timestep are investigated. The unstructured PIC code is applied to the simulation of Field Emission Array (FEA) cathodes. Electron injection conditions are obtained from a Field Emission microtip model and the simulation domain includes the FEA cathode and anode. Currents collected by the electrodes are compared to theoretical values. Simulations show the formation of the virtual cathode and three-dimensional effects under certain injection conditions. The unstructured PIC code is also applied to the simulation of a micro-Retarding Potential Analyzer. For simple cases the current at the collector plate is compared favorably with theoretical predictions. The simulations show the complex structure of the potential inside the segmented microchannel, the phase space of plasma species and the space-charge effects not captured by the theory.

This work investigates numerically the process of Teflon ablation using a finite-volume discretization, implicit time integration and a domain decomposition method in three-dimensions. The interest in Teflon stems from its use in Pulsed Plasma Thrusters and in thermal protection systems for reentry vehicles. The ablation of Teflon is a complex process that involves phase transition, a receding external boundary where the heat flux is applied, an interface between a crystalline and amorphous (gel) phase and a depolymerization reaction which happens on and beneath the ablating surface. The mathematical model used in this work is based on a two-phase model that accounts for the amorphous and crystalline phases as well as the depolymerization of Teflon in the form of an Arrhenius reaction equation. The model accounts also for temperature-dependent material properties, for unsteady heat inputs and boundary conditions in 3D. The model is implemented in 3D domains of arbitrary geometry with a finite volume discretization on unstructured grids. The numerical solution of the transient reaction-diffusion equation coupled with the Arrhenius-based ablation model advances in time using implicit Crank-Nicolson scheme. For each time step the implicit time advancing is decomposed into multiple sub-problems by a domain decomposition method. Each of the sub-problems is solved in parallel by Newton-Krylov non-linear solver. After each implicit time-advancing step, the rate of ablation and the fraction of depolymerized material are updated explicitly with the Arrhenius-based ablation model. After the computation, the surface of ablation front and the melting surface are recovered from the scalar field of fraction of depolymerized material and the fraction of melted material by post-processing. The code is verified against analytical solutions for the heat diffusion problem and the Stefan problem. The code is validated against experimental data of Teflon ablation. The verification and validation demonstrates the ability of the numerical method in simulating three dimensional ablation of Teflon.

Borders of flow field around immersed bodies can be extended to long distances since there are no physical boundaries. In computational practice however, the flow domain must be restricted to a reasonable size by imposing appropriate boundary conditions at the edges of the computational space. In this thesis work, streamlines obtained from potential flow solution in a relatively large spatial domain are utilized to specify the boundaries and boundary conditions for a more restricted computational domain to be used for detailed viscous flow computations. A grid generation code is adopted for generation of unstructured triangular grid systems for domains involving multiple immersed bodies of any shape at arbitrary orientations such as a group of tall buildings in horizontal plane. Finite volume method is used in the solution of Laplace equation for the stream function. A deformation modulus is introduced as a probe parameter to aid locating the viscous flow boundaries. The computer code acts as a preprocessor for viscous flow computations, specifying the computational boundaries, the boundary conditions and generating the computational grid.

The multigrid technique is one of the most effective techniques to achieve the reduction of the CPU cost for flow solvers. The multigrid strategy uses the multilevel grids which are the coarsening subsets of fine grid. An explicit solver rapidly reduces the high frequency errors on the computational grids. Since high frequency errors on coarse grids correspond to low frequency errors on fine grids, cycling through the coarse grid levels rapidly reduces the errors ranging from high-to-low frequency. The aim of this study is, therefore, to accelerate SENSE3D solver developed by TUBITAK-SAGE by implementating multigrid concept. In this work, a novel grid coarsening method suitable for cell-centered hybrid/unstructured grids is developed to provide the cells with high aspect ratio. This new grid coarsening technique relies on the agglomeration of cells based on their distribution on octree data structure. Then, the multigrid strategy is implemented to the baseline flow solver. During this implementation, the flux calculation along the face loops is modified without changing cell-centered scheme. The performance of the coarsening algorithm is investigated for all grid types in two and three dimension. The grid coarsening algorithm produces well defined, nested, body fitted coarser grids with aspect ratios of one and the coarse grids have similar characteristics of Cartesian grids. Then, the multigrid flow solutions are obtained at inviscid, laminar and turbulent flows. It is shown that, the convergence accelerations are up to 14 times for inviscid flows and in a range of 4 to 110 fold for turbulent flow solutions.

Compositional simulation is a complex task that involves solving several equations simultaneously for all grid blocks representing a petroleum reservoir. Usually, these equations are separated into two groups: primary and secondary equations. Similarly, the unknowns of the system are also separated into primary and secondary variables. Considering the large number of unknowns, there are many ways to separate such variables in order to deal with the primary variables. This work aims at comparing a number of formulations for compositional reservoir simulation. It also aims at enhancing the formulations with new features not provided in the original publications. To accomplish these objectives, various formulations prevailing in the literature are implemented in The University of Texas at Austin in-house fully implicit simulator named GPAS (General Purpose Adaptive Simulator) and their performances were compared. Subsequently, some of the formulations were enhanced and tested for various applications. The comparison of the formulations studied indicated differences in efficiency for each approach. These differences come from the fact that when one is solving for a different set of primary variables, the manipulation of the equations is analogous to the use of a preconditioner applied to a linear system of equations. Furthermore, unlike a preconditioner, changing the primary variables affects the non-linear solver. Therefore, differences in terms of the number of Newton-Raphson iterations, used for solution of nonlinear equations resulting from discretization of nonlinear partial differential equations representing fluid flow in the reservoir, are expected. In addition to these differences in the non-linear solver, many formulations explore the fact that a reduced number of equations need to be solved implicitly, thus considerably reducing the CPU time dedicated to the linear solver. Finally, new features not provided in the original published formulations such as three-phase flash calculation, physical dispersion, and unstructured grid were implemented and verified. Additionally, it was demonstrated that, in certain situations, these enhancements are essential to properly model the physical phenomena occurring in oil and gas reservoirs. / text

A growing demand for more detailed modeling of subsurface physics as ever more challenging reservoirs - often unconventional, with significant geomechanical particularities - become production targets has moti-vated research in coupled flow and geomechanics. Reservoir rock deforms to given stress conditions, so the simplified approach of using a scalar value of the rock compressibility factor in the fluid mass balance equation to describe the geomechanical system response cannot correctly estimate multi-dimensional rock deformation. A coupled flow and geomechanics model considers flow physics and rock physics simultaneously by cou-pling different types of partial differential equations through primary variables. A number of coupled flow and geomechanics simulators have been developed and applied to describe fluid flow in deformable po-rous media but the majority of these coupled flow and geomechanics simulators have limited capabilities in modeling multiphase flow and geomechanical deformation in a heterogeneous and fractured reservoir. In addition, most simulators do not have the capability to simulate both coarse and fine scale multiphysics. In this study I developed a new, fully implicit multiphysics simulator (TAM-CFGM: Texas A&M Coupled Flow and Geomechanics simulator) that can be applied to simulate a 2D or 3D multiphase flow and rock deformation in a heterogeneous and/or fractured reservoir system. I derived a mixed finite element formu-lation that satisfies local mass conservation and provides a more accurate estimation of the velocity solu-tion in the fluid flow equations. I used a continuous Galerkin formulation to solve the geomechanics equa-tion. These formulations allowed me to use unstructured meshes, a full-tensor permeability, and elastic stiffness. I proposed a numerical upscaling of the permeability and of the elastic stiffness tensors to gener-ate a coarse-scale description of the fine-scale grid in the model, and I implemented the methodology in the simulator. I applied the code I developed to the simulation of the problem of multiphase flow in a fractured tight gas system. As a result, I observed unique phenomena (not reported before) that could not have been deter-mined without coupling. I demonstrated the importance and advantages of using unstructured meshes to effectively and realistically model a reservoir. In particular, high resolution discrete fracture models al-lowed me to obtain more detailed physics that could not be resolved with a structured grid. I performed numerical upscaling of a very heterogeneous geologic model and observed that the coarse-scale numerical solution matched the fine scale reference solution well. As a result, I believed I developed a method that can capture important physics of the fine-scale model with a reasonable computation cost.

<p>Computational Fluid Dynamic (CFD) simulations often produce datasets defined over unstructured grids with solid boundaries. Though unstructured grids allow for the flexible representation of this geometry and the refinement of the grid resolution, they suffer from high storage cost, non-trivial spatial queries, and low reconstruction smoothness. Rectilinear grids, in contrast, have a negligible memory footprint and readily support smooth data reconstruction, though with reduced geometric flexibility.</p><p>This thesis is concerned with the creation of accurate reconstruction of large unstructured datasets on rectilinear grids with the capability of representing complex boundaries. We present an efficient method to automatically determine the geometry of a rectilinear grid upon which a low-error data reconstruction can be achieved with a given reconstruction kernel. Using this rectilinear grid, we address the potential ill-posedness of the data fitting problem, as well as the necessary balance between smoothness and accuracy, through a bi-level smoothness regularization. To tackle the computational challenge posed by very large input datasets and high-resolution reconstructions, we propose a block-based approach that allows us to obtain a seamless global approximation solution from a set of independently computed sparse least-squares problems. </p><p></p><p>We endow the approximated rectilinear grid with boundary handling capabilities that allows for accommodating challenging boundaries while supporting high-order reconstruction kernels. Results are presented for several 3D datasets that demonstrate the quality of the visualization results that our reconstruction enables, at a greatly reduced computational and memory cost. Our data representation enjoys all the benefits of conventional rectilinear grids while addressing their fundamental geometric limitations.</p>