The method of fundamental solutions for some direct and inverse problems

We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require mesh generation or integration over the solution boundary, making it suitable for solving inverse problems, like the BHCP, an ill-posed problem. We extend the MFS proposed in Johansson and Lesnic (2008) for the direct one-dimensional heat equation, and Johansson and Lesnic (2009) for the direct one-phase one-dimensional Stefan problem, with source points placed outside the space domain of interest and in time. Theoretical properties, including linear independence and denseness, the placement of source points, and numerical investigations are included showing that accurate results can be efficiently obtained with small computational cost. Regularization techniques, in particular, Tikhonov regularization, in conjunction with the L-curve criterion, are used to solve the illconditioned systems generated by this method. In Chapters 6 and 8, investigating the linear and nonlinear Stefan problems, the MATLAB toolbox lsqnonlin, which is designed to minimize a sum of squares, is used

Theoretical studies in support of the 3M-vapor transport (PVTOS-) experiments

Results are reported for a preliminary theoretical study of the coupled mass-, momentum-, and heat-transfer conditions expected within small ampoules used to grow oriented organic solid (OS-) films, by physical vapor transport (PVT) in microgravity environments. It is show that previous studies made restrictive assumptions (e.g., smallness of delta T/T, equality of molecular diffusivities) not valid under PVTOS conditions, whereas the important phenomena of sidewall gas creep, Soret transport of the organic vapor, and large vapor phase supersaturations associated with the large prevailing temperature gradients were not previously considered. Rational estimates are made of the molecular transport properties relevant to copper-phthalocyanine monomeric vapor in a gas mixture containing H2(g) and Xe(g). Efficient numerical methods have been developed and are outlined/illustrated here to making steady axisymmetric gas flow calculations within such ampoules, allowing for realistic realistic delta T/T(sub)w-values, and even corrections to Navier-Stokes-Fourier 'closure' for the governing continuum differential equations. High priority follow-on studies are outlined based on these new results

Supersonic quasi-axisymmetric vortex breakdown

An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated

DNS of bifurcations in an air-filled rotating baroclinic annulus

Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics and a route to chaos in a rotating fluid subjected to lateral heating is presented here and discussed in the context of laboratory experiments in the baroclinic annulus. Following two previous preliminary studies by Maubert and Randriamampianina, the fluid used is air rather than a liquid as used in all other previous work. This study investigated a bifurcation sequence from the axisymmetric flow to a number of complex flows. The transition sequence, on increase of the rotation rate, from the axisymmetric solution via a steady, fully-developed baroclinic wave to chaotic flow followed a variant of the classical quasi-periodic bifurcation route, starting with a subcritical Hopf and associated saddle-node bifurcation. This was followed by a sequence of two supercritical Hopf-type bifurcations, first to an amplitude vacillation, then to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and finally to a chaotic MAV\@. In the context of the baroclinic annulus this sequence is unusual as the vacillation is usually found on decrease of the rotation rate from the steady wave flow. Further transitions of a steady wave with a higher wave number pointed to the possibility that a barotropic instability of the side wall boundary layers and the subsequent breakdown of these barotropic vortices may play a role in the transition to structural vacillation and, ultimately, geostrophic turbulence.Comment: 31 page

Numerical simulation of buoyancy-induced flow in a sealed rotating cavity

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN025326 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Development of a conjugate heat transfer solver

The current research study presents a numerical approach in modelling the conjugate heat transfer system of the gas-turbine rotating discs-cavities. The work was undertaken to understand such phenomena and, more specifically, to numerically investigate the thermal interactions in rotating discs-cavities. The developed solver is capable of dealing with complex heat transfer problems, such as unsteady three-dimensional compressible rotating-flows. The development was based on integrating an inhouse computational fluid dynamics code (SURF) with a heat conduction solver internally. Method of interpolation using mapped area was also introduced for treating non-matching meshes at interface, which plays an effective role in exchanging boundary data. This thesis also documents the development of a numerical finite volume cell-vertex hybrid edgebased heat conduction code by the author using FORTRAN. The heat conduction solver was developed and validated to deal with three dimensional solid-domains using unstructured elements. The validation process was carried out on several test cases for investigating the temperature distribution. The test results were presented to show good agreement with the analytical, experimental and other commercial numerical solutions where they exist

The Dependence of the Time-Asymptotic Structure of 3-D Vortex Breakdown on Boundary and Initial Conditions

The three-dimensional, compressible Navier-Stokes equations are solved numerically to simulate vortex breakdown in tubes. Time integration is performed with an implicit Beam-Warming algorithm, which uses fourth-order compact operators to discretize spatial derivatives. Initial conditions are obtained by solving the steady, compressible, and axisymmetric form of the Navier-Stokes equations using Newton\u27s method. Stability of the axisymmetric initial conditions is assessed through 3-D time integration. Unique axisymmetric solutions at a Reynolds number of 250 lose stability to 3-D disturbances at a critical value of vortex strength, resulting in 3-D and time-periodic flow. Axisymmetric solutions at a Reynolds number of 1000 contain regions of nonuniqueness. Within this region, 3-D time integration reveals only unique solutions, with nonunique, axisymmetric initial conditions converging to a unique solution that is steady and axisymmetric. Past the primary limit point, which approximately identifies critical flow, the solutions bifurcate into 3-D periodic flows

An international code comparison study on coupled thermal, hydrologic and geomechanical processes of natural gas hydrate-bearing sediments

Highlights • Code comparisons build confidence in simulators to model interdependent processes. • International hydrate reservoir simulators are compared over five complex problems. • Geomechanical processes significantly impact response of gas hydrate reservoirs. • Simulators yielded comparable results, however many differences are noted. • Equivalent constitutive models are required to achieve agreement across simulators. Geologic reservoirs containing gas hydrate occur beneath permafrost environments and within marine continental slope sediments, representing a potentially vast natural gas source. Numerical simulators provide scientists and engineers with tools for understanding how production efficiency depends on the numerous, interdependent (coupled) processes associated with potential production strategies for these gas hydrate reservoirs. Confidence in the modeling and forecasting abilities of these gas hydrate reservoir simulators (GHRSs) grows with successful comparisons against laboratory and field test results, but such results are rare, particularly in natural settings. The hydrate community recognized another approach to building confidence in the GHRS: comparing simulation results between independently developed and executed computer codes on structured problems specifically tailored to the interdependent processes relevant for gas hydrate-bearing systems. The United States Department of Energy, National Energy Technology Laboratory, (DOE/NETL), sponsored the first international gas hydrate code comparison study, IGHCCS1, in the early 2000s. IGHCCS1 focused on coupled thermal and hydrologic processes associated with producing gas hydrates from geologic reservoirs via depressurization and thermal stimulation. Subsequently, GHRSs have advanced to model more complex production technologies and incorporate geomechanical processes into the existing framework of coupled thermal and hydrologic modeling. This paper contributes to the validation of these recent GHRS developments by providing results from a second GHRS code comparison study, IGHCCS2, also sponsored by DOE/NETL. IGHCCS2 includes participants from an international collection of universities, research institutes, industry, national laboratories, and national geologic surveys. Study participants developed a series of five benchmark problems principally involving gas hydrate processes with geomechanical components. The five problems range from simple geometries with analytical solutions to a representation of the world's first offshore production test of methane hydrates, which was conducted with the depressurization method off the coast of Japan. To identify strengths and limitations in the various GHRSs, study participants submitted solutions for the benchmark problems and discussed differing results via teleconferences. The GHRSs evolved over the course of IGHCCS2 as researchers modified their simulators to reflect new insights, lessons learned, and suggested performance enhancements. The five benchmark problems, final sample solutions, and lessons learned that are presented here document the study outcomes and serve as a reference guide for developing and testing gas hydrate reservoir simulators