Geology topics

T. V. Hromadka

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

14 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↗

USGS1987

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 approximate boundary generation. Consequently, 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.

Journal of Offshore Mechanics and Arctic Engineeri↗

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

Determining relative error bounds for the CVBEM

The Complex Variable Boundary Element Methods provides a measure of relative error which can be utilized to subsequently reduce the error or provide information for further modeling analysis. By maximizing the relative error norm on each boundary element, a bound on the total relative error for each boundary element can be evaluated. This bound can be utilized to test CVBEM convergence, to analyze the effects of additional boundary nodal points in reducing the modeling error, and to evaluate the sensitivity of resulting modeling error within a boundary element from the error produced in another boundary element as a function of geometric distance.

Engineering Analysis↗

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↗

USGS1985

MODELING HYDRAULIC PROBLEMS USING THE CVBEM AND THE MICROCOMPUTER.

The Complex Variable Boundary Element Method (CVBEM) offers an effective and efficient means for modeling two-dimensional potential and related flow problems. The method has been applied to various hydraulic and hydrodynamic problems - surface water, ground water, and other flows - and has proven its accuracy, reliability and usefulness. The paper describes the CVBEM and its application.

Conference Paper↗

USGS1985

Algorithm to reduce approximation error from the complex-variable boundary-element method applied to soil freezing.

An algorithm is presented for the numerical solution of the Laplace equation boundary-value problem, which is assumed to apply to soil freezing or thawing. The Laplace equation is numerically approximated by the complex-variable boundary-element method. The algorithm aids in reducing integrated relative error by providing a true measure of modeling error along the solution domain boundary. This measure of error can be used to select locations for adding, removing, or relocating nodal points on the boundary or to provide bounds for the integrated relative error of unknown nodal variable values along the boundary.

Numerical heat transfer↗

USGS1985

SOLVING THE TWO-DIMENSIONAL DIFFUSION FLOW MODEL.

A simplification of the two-dimensional (2-D) continuity and momentum equations is the diffusion equation. To investigate its capability, the numerical model using the diffusion approach is applied to a hypothetical failure problem of a regional water reservoir. The model is based on an explicit, integrated finite-difference scheme, and the floodplain is simulated by a popular home computer which supports 64K FORTRAN. Though simple, the 2-D model can simulate some interesting flooding effects that a 1-D full dynamic model cannot.

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

The complex variable boundary element method: Applications in determining approximative boundaries

The complex variable boundary element method (CVBEM) is used to determine approximation functions for boundary value problems of the Laplace equation such as occurs in potential theory. By determining an approximative boundary upon which the CVBEM approximator matches the desired constant (level curves) boundary conditions, the CVBEM is found to provide the exact solution throughout the interior of the transformed problem domain. Thus, the acceptability of the CVBEM approximation is determined by the closeness-of-fit of the approximative boundary to the study problem boundary.

Engineering Analysis↗

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↗