USE OF A GENERAL PARTIAL DIFFERENTIAL EQUATION SOLVER FOR SOLUTION OF HEAT AND MASS TRANSFER PROBLEMS IN SOILS
Pentland, Jason S
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The application of geotechnical principles to linear infrastructure developments, such as pipelines, has often been neglected due to the high cost of analysis. The requirements of producing geotechnical analyses inexpensively demand that new techniques be developed. Development of general partial differential equation solvers represents a tool by which these analyses can be performed. The objective of this research is to apply general partial differential equations solvers to the problem of heat and mass transfer in soils. Solutions using the general partial differential equation solver called FlexPDE (PDE Solutions, 1999)are compared with analytical and accepted numerical solutions of the problems. The FlexPDE program was first verified against see page problems analyzed using the program Seep/W. The results obtained showed that FlexPDE correctly solves seepage problems. The descriptor files of Nguyen (1999) for the PDEase2D program used in this stage showed that FlexPDE and PDEase2D produce similar results. The three dimensional capabilities of FlexPDE demonstrated in a simple steady state example show an increased versatility of the FlexPDE program over PDEase2D. Solution of conductive heat flow using FlexPDE showed that realistic functions of the soil-freezing curve are needed to ensure convergence. The FlexPDE solutions to the Neumann problem for conductive heat flow in a material undergoing phase change were compared to the Temp/W model. The Temp/W results were similar to the FlexPDE results provided the same interpretation of the slope of the soil-freezing curve, m1/2, was used in both programs. Solution of coupled heat and mass transfer in the present study attempted to use the theory developed by Wilson (1990)as modified by Joshi (1993). Successful modelling of coupled heat and mass transfer was achieved in FlexPDE for cases where the gradients acting in the soil were relatively small. Large gradients, such as those occurring during evaporation from the soil surface,were not modelled satisfactorily in FlexPDE. A methodology for using FlexPDE for practical engineering problems is included in this study. The methodology shows how use of a general partial differential equation solver allows the engineer flexibility in in putting the phenomena studied, material properties, problem geometry, and boundary conditions. This example specifically deals with the pipeline industry. The example shows how FlexPDE and similar programs are applicable for solving problems in practical geotechnical engineering. The example relates the theory and application presented in the thesis to the original objectives.