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Application of Hardy's multiquadric interpolation to hydrodynamics

Description: Hardy's multiquadric interpolation (MQI) scheme is a global, continuously differentiable interpolation method for solving scattered data interpolation problems. It is capable of producing monotonic, extremely accurate interpolating functions, integrals, and derivatives. Derivative estimates for a variety of one and two-dimensional surfaces were obtained. MQI was then applied to the spherical blast wave problem of von Neumann. The numerical solution agreed extremely well with the exact solution. 17 refs., 3 figs., 2 tabs.
Date: October 1, 1985
Creator: Kansa, E.J.
Partner: UNT Libraries Government Documents Department

Verification of the NIKE3D structural analysis code by comparison against the analytic solution for a spherical cavity under a far-field uniaxial stress

Description: The original scope of this task was to simulate the stresses and displacements of a hard rock tunnel experimental design using a suitable three-dimensional finite element code. NIKE3D was selected as a suitable code for performing these primarily approximate linearly elastic 3D analyses, but it required modifications to include initial stress, shear traction boundary condition and excavation options. During the summer of 1988, such capabilities were installed in a special version of NIKE3D. Subsequently, we verified both the LLNL's commonly used version of NIKE3D and our private modified version against the analytic solution for a spherical cavity in an elastic material deforming under a far-field uniaxial stress. We find the results produced by the unmodified and modified versions of NIKE3D to be in good agreement with the analytic solutions, except near the cavity, where the errors in the stress field are large. As can be expected from a code based on a displacement finite element formulation, the displacements are much more accurate than the stresses calculated from the 8-noded brick elements. To reduce these errors to acceptable levels, the grid must be refined further near the cavity wall. The level of grid refinement required to simulate accurately tunneling problems that do not have spatial symmetry in three dimensions using the current NIKE3D code is likely to exceed the memory capacity of the largest CRAY 1 computers at LLNL. 8 refs., 121 figs.
Date: January 1, 1989
Creator: Kansa, E.J.
Partner: UNT Libraries Government Documents Department

Time-dependent buoyant puff model for explosive sources

Description: This paper presents a new model for explosive puff rise histories that is derived from the strong conservative form of the partial differential equations of mass, momenta, and total energy that are integrated over space to yield a coupled system of time dependent nonlinear ordinary differential equations (ODEs). By allowing the dimensions of the puff to evolve laterally and horizontally, the initial rising spherical shaped puff evolves into a rising ellipsoidal shaped mushroom cloud. This model treats the turbulence that is generated by the puff itself and the ambient atmospheric turbulence as separate mechanisms in determining the puff history. The puff rise history was found to depend not only upon the mass and initial temperature of the explosion, but also upon the local stability conditions of the ambient atmosphere through which the puff rises. This model was calibrated by comparison with the Roller Coaster experiments, ranging from unstable to very stable atmospheric conditions; the agreement of the model history curves with these experimental curves was within 10%.
Date: October 1, 1997
Creator: Kansa, E.J.
Partner: UNT Libraries Government Documents Department

Time-dependent buoyant puff model for explosive sources

Description: Several models exist to predict the time dependent behavior of bouyant puffs that result from explosions. This paper presents a new model that is derived from the strong conservative form of the conservation partial differential equations that are integrated over space to yield a coupled system of time dependent nonlinear ordinary differential equations. This model permits the cloud to evolve from an intial spherical shape not an ellipsoidal shape. It ignores the Boussinesq approximation, and treats the turbulence that is generated by the puff itself and the ambient atmospheric tubulence as separate mechanisms in determining the puff history. The puff cloud rise history was found to depend no only on the mass and initial temperature of the explosion, but also upon the stability conditions of the ambient atmosphere. This model was calibrated by comparison with the Roller Coaster experiments.
Date: January 1997
Creator: Kansa, E. J.
Partner: UNT Libraries Government Documents Department

Stress-strain gage measurements on a Nevada Test Site (NTS) event using pairs of triple foil gages

Description: A triple-material stress-strain gage containing foils of ytterbium, manganin, and constantan was tested at LLNL. This gage yields three independent piezoresistance measurements from which an independent set of principal strains and principal stresses can be inferred. We have analyzed the signals from a gage at a specific location buried at a distance from the center of energy of an event at NTS. We inverted the resistivity signals to calculate the stress and strain histories as sensed by the foils. Using the elastic material properties and the traction and displacement conditions at the various material interfaces from the foils to the host geological medium, we calculated the stress and strain histories in the host geological medium. However, because of uncertainties in the elastic properties of the layers of surrounding materials, we calculated significant variations in both the peaks and signatures of the stress and strain histories that could produce the foil stress and strain histories. We conclude that, because of the inclusion problem, accurate measurements of the stress-strain histories in the host geological medium can be adequately addressed only by minimizing, as much as possible, such uncertainties.
Date: November 30, 1990
Creator: Kansa, E.J. & Stout, R.B.
Partner: UNT Libraries Government Documents Department

Geomechanics investigations in support of the large block test at Fran Ridge, Nye County, Nevada.

Description: The Yucca Mountain Site Characterization Project is investigating the Topopah Spring Tuff at Yucca Mountain, Nevada for its suitability as a host rock for the disposal of high level nuclear wastes. The Lawrence Livermore National Laboratory is planning a large block test (LBT) to investigate coupled thermal-mechanical-hydrological and geochemical processes that may occur in the repository near-field environment.
Date: July 21, 1994
Creator: Blair, S.C.; Berge, P.; Kansa, E.; Lin, Wunan & Roberts, J.
Partner: UNT Libraries Government Documents Department

Grain and burnup dependence of spent fuel oxidation: geological repository impact

Description: Further refinements to the oxidation model of Stout et al. have been made. The present model incorporates the burnup dependence of the oxidation rate in addition to an allowance for a distribution of grain sizes. The model was tested by comparing the model results with the oxidation histories of spent fuel samples oxidized in Thermogravimetric Analysis (TGA) or Oven Dry-Bath (ODB) experiments. The comparison between the experimental and model results are remarkably close and confirm the assumption that grain-size distributions and activation energies are the important parameters to predicting oxidation behavior. The burnup dependence of the activation energy was shown to have a greater effect than decreasing the effective grain size in suppressing the rate of the reaction U{sub 4}O{sub 9}(rightwards arrow)U{sub 3} O{sub 4}. Model results predict that U{sub 3}O{sub 8} formation of spent fuels exposed to oxygen will be suppressed even for high burnup fuels that have undergone restructuring in the rim region, provided the repository temperature is kept sufficient.
Date: October 15, 1998
Creator: Hanson, B. D.; Kansa, E. J. & Stoot, R.B.
Partner: UNT Libraries Government Documents Department

The method of Laplace Transform MultiQuadrics (LTMQ) for the solution of the groundwater flow equation

Description: This paper presents a new numerical method, the Laplace Transform MultiQuadrics (LTMQ) method, developed for the solution of the diffusion-type parabolic Partial Differential Equation (PDE) of fluid flow through porous media. LTMQ combines a MultiQuadrics (MQ) approximation scheme with a Laplace transform formulation. The use of MQ in the spatial approximations allows the accurate description of problems in complex porous media with a very limited number of nodes. The Laplace transform formulation eliminates the need for time discretization, thus allowing an unlimited time step size without any loss of accuracy. LTMQ is tested against results from three test problems of groundwater flow obtained from a standard Finite Difference (FD) model, as well as from analytical solutions. An excellent agreement between the LTMQ and the analytical and FD solutions is observed, while significant reductions in computer execution times may be achieved.
Date: June 1, 1992
Creator: Moridis, G.J. (Lawrence Berkeley Lab., CA (United States)) & Kansa, E. (Lawrence Livermore National Lab., CA (United States))
Partner: UNT Libraries Government Documents Department