Two- and Three-Dimensional Finite Element Groundwater Flow
Models with Isothermal Freezing and Thawing
H.D. McInvale, T.V. Hromadka II, M. Phillips, B. Landry
During the summer, cadets at the United States Military Academy at West Point can choose to participate in an Advanced Individual Academic Development (AIAD) program. For the three following proposed projects, the AIAD program provides cadets with an opportunity to observe and implement concepts from their course work in computational engineering mathemat- ics with an immersion experience during a summer internship. The AIAD program enables cadets to work alongside leaders in government and industry both stateside and abroad. The funding and coordination for these projects is through the AIAD program at West Point and is an element of the computational engineering mathematics theme at the West Point Department of Mathematical-Sciences. The described research and development work will be completed during the summer 2016 session.
Introduction
In the current project, ongoing work involves application of the finite element method (FEM) applied to solving heat and groundwater flow transport in algid climates where soil water freezes and thaws isothermally. A two- and three- dimensional FEM computer program is being developed for application towards engineering and planning studies where freezing and thawing of algid soils is of concern. The computer code being focused upon models groundwater flow and also heat transport in a two- or three-dimensional domain. Because the computer program is intended for appli- cations involving freezing and thawing of algid soils, the freezing process dehy- drates the soil at the freezing front (the location where phase change is occur- ring) which, in turn, draws towards the freezing front soil water from areas in the soil where soil water can be mobilized to move towards lower soil pore pressure. The code applies in general, therefore multiple freezing and thawing fronts can occur within the problem domain. Basic description of these transport processes are provided in the figures included.
Objectives of Project
The target project will be completed during the summer 2016 session. This particular topic involves aspects of both
engineering-mathematics and computa- tional geosciences.
The main objectives of this project are fivefold:
(1) Provide the theoretical and modeling background used in a two-dimen- sional and three-dimensional model of heat and soil-water flow, coupled by soil-water freezing and thawing;
(2) Present the major modeling assump- tions used in the computer program, and the various components of the program in order to aid the end-user in the use of the model;
(3) Present the necessary parameters and data requirements used in the computer model;
(4) Discuss the computer model output product, and methods to interpret the results; and
(5) Present the data input sequence to the computer model.
Project Computer Program Documentation Organization
The Documentation report will be organized into five chapters and one appendix:
Chapter 1 Introduction to the project and report.
Chapter 2 Development of the Nodal Domain Integration (NDI) model
of two-dimensional soil-water flow in saturated and unsaturated soils.
Chapter 3 Development of the NDI model for heat flow in three dimen- sions. The third dimension is included in this NDI development in order to provide for the extension of the phase change model to other coordinate systems (an NDI analog for radial coordinates is presented in Appendix A) .
Chapter 4 Development of the two-dimensional soil-water phase change model used to couple the heat and soil-water flow during soil-water freezing and thawing.
Chapter 5 Summary of the two- dimensional freezing/thawing model and the modeling input-output charac- teristics. Provides documentation to the computer program input requirements.
Appendix Explanation of the heat flow modeling approach developed in Chapter 3 to radial coordinates. The theory developed herein applies to both heat and soil-water flow in the selection of mass-lumping factors for use in NDI domain models.
Computational Mathematical Model Description
A problem of interest is the design and maintenance of roadways construct- ed in algid climates where freeze and thaw degradation results in collapse
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