Geology topics

T. V. Hromadka

Publications and source records attributed to T. V. Hromadka.

8 recordsLinked to original sources

USGS2005

Reducing relative error from the CVBEM by proper treatment of the known boundary conditions

By a proper treatment of the known boundary conditions of a boundary value problem, a complex variable boundary element method (CVBEM) can be used to exactly satisfy the known nodal point boundary values. In this fashion, a numerical model can be developed which generates relative error information along the problem boundary that can be used to reduce the modelling error by either an integrated measure or a maximum relative error measure.

International Journal for Numerical Methods in Eng↗

USGS2005

The complex variable boundary element method: Applications

The complex variable boundary element method (CVBEM) is used to approximate several potential problems where analytical solutions are known: A modelling result produced from the CVBEM is a measure of relative error in matching the known boundary condition values of the problem. A CVBEM error-reduction algorithm is used to reduce the relative error of the approximation by adding nodal points in boundary regions where error is large. From the-test problems, overall error is reduced significantly by utilizing the adaptive integration algorithm.

International Journal for Numerical Methods in Eng↗

USGS1986

Predicting two-dimensional steady-state soil freezing fronts using the CVBEM

The complex variable boundary element method (CVBEM) is used instead of a real variable boundary element method due to the available modeling error evaluation techniques developed. The modeling accuracy is evaluated by the model-user in the determination of an approximative boundary upon which the CVBEM provides an exact solution. Although inhomogeneity (and anisotropy) can be included in the CVBEM model, the resulting fully populated matrix system quickly becomes large. Therefore in this paper, the domain is assumed homogeneous and isotropic except for differences in frozen and thawed conduction parameters on either side of the freezing front. The example problems presented were obtained by use of a popular 64K microcomputer (the current version of the program used in this study has the capacity to accommodate 30 nodal points).

Journal of Heat Transfer↗

USGS1985

Locating CVBEM collocation points for steady state heat transfer problems

The Complex Variable Boundary Element Method or CVBEM provides a highly accurate means of developing numerical solutions to steady state two-dimensional heat transfer problems. The numerical approach exactly solves the Laplace equation and satisfies the boundary conditions at specified points on the boundary by means of collocation. The accuracy of the approximation depends upon the nodal point distribution specified by the numerical analyst. In order to develop subsequent, refined approximation functions, four techniques for selecting additional collocation points are presented. The techniques are compared as to the governing theory, representation of the error of approximation on the problem boundary, the computational costs, and the ease of use by the numerical analyst.

Engineering Analysis↗

USGS1985

A two-dimensional dam-break flood plain model

A simple two-dimensional dam-break model is developed for flood plain study purposes. Both a finite difference grid and an irregular triangle element integrated finite difference formulation are presented. The governing flow equations are approximately solved as a diffusion model coupled to the equation of continuity. Application of the model to a hypothetical dam-break study indicates that the approach can be used to predict a two-dimensional dam-break flood plain over a broad, flat plain more accurately than a one-dimensional model, especially when the flow can break-out of the main channel and then return to the channel at other downstream reaches. ?? 1985.

Advances in Water Resources↗

USGS1985

ANALYZING NUMERICAL ERRORS IN DOMAIN HEAT TRANSPORT MODELS USING THE CVBEM.

Besides providing an exact solution for steady-state heat conduction processes (Laplace Poisson equations), the CVBEM (complex variable boundary element method) can be used for the numerical error analysis of domain model solutions. For problems where soil water phase change latent heat effects dominate the thermal regime, heat transport can be approximately modeled as a time-stepped steady-state condition in the thawed and frozen regions, respectively. The CVBEM provides an exact solution of the two-dimensional steady-state heat transport problem, and also provides the error in matching the prescribed boundary conditions by the development of a modeling error distribution or an approximative boundary generation. This error evaluation can be used to develop highly accurate CVBEM models of the heat transport process, and the resulting model can be used as a test case for evaluating the precision of domain models based on finite elements or finite differences.

Conference Paper↗

USGS1984

A simple model of ice segregation using an analytic function to model heat and soil-water flow

For slowly moving freezing fronts in soil, the heat-transport equation may be approximated by the Laplacian of temperature. Consequently, potential theory may be assumed to apply and the temperature state can be approximated by an analytic function. The movement of freezing fronts may be approximated by a time-stepped solution of the phase-change problem, thus solving directly for heat flow across a freezing or thawing front. Moisture transport may approximated by using an exact solution of the moisture-transport equation assuming quasi-steady-state conditions, appropriate boundary conditions, and an exponential function relating unsaturated hydraulic conductivity (defined within the thawed zones) to pore water pressure (tension). This approach is used to develop a single model of ice segregation (frost-heave) in freezing soils. Applications to published and experimental one-dimension soil column freezing data show promising results.

Journal of Energy Resources Technology, Transactio↗

USGS1984

A simple model of a phreatic surface through an earth dam

A simple numerical model for estimating a phreatic surface in an earthen dam is presented. The numerical approach is based upon the Complex Variable Boundary Element Method (CVBEM). By expanding the CVBEM approximation geometric functions into a first order Taylor series, the unknown phreatic surface location geometrics can be approximated without iteration by solving a single matrix system. The developed technique provides for the numerical solution of the inverse problem of locating the phreatic surface coordinates. A comparison of results produced from this simple approach to results produced from a finite element analog and an iterative CVBEM analog for an example problem is presented.

Advances in Water Resources↗