Sundaraelangovan Selvam | Delft University of Technology (original) (raw)
A dynamic researcher willing to explore and learn new things in research.
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Address: Delfgauw,
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Master thesis by Sundaraelangovan Selvam
In this project, the evolution and fundamentals of Theory of Porous Media are studied. The field ... more In this project, the evolution and fundamentals of Theory of Porous Media are studied. The field equations governing the dynamic response of a fluid-saturated elastic porous medium with intrinsically incompressible solid and fluid constituents are derived and analyzed. The results of the governing field equations are treated numerically using Standard Galerkin procedure and the Finite element method. This class of problems comes under volumetrically coupled problems due to the solid-fluid momentum interaction that involves a coupling between the momentum equations and the incompressibility constraint. In this concern, two numerical examples are considered (one-and two-dimensional wave propagation example). These examples are tested numerically using multi-field formulations feasible in porous media dynamics. The tests are carried out under different combination of approximation order of the individual unknowns with several refinement levels of mesh and different time-step sizes. Here the degree of coupling is controlled by the permeability parameter, so each test cases are carried out with both large and small permeability values. In the first numerical example, firstly the analytical solution of the fluid-saturated poroelastic medium is derived using Laplace transformation and the solutions of the unknown variables are found using MAPLE programming. Then, the solutions of different formulations,which are analyzed numerically, are compared with the analytical solution for solid displacement and pore-fluid pressure through error calculation. These error values of each test cases are plotted graphically against different time-step sizes and different mesh sizes. In the second numerical example, the propagation of solid displacement and pore-fluid pressure waves inside a porous medium is studied and the results are plotted graphically. The in-plane motion of the displacements and the pressure oscillations are compared between different formulations and polynomial degrees combinations. In conclusion, the best formulation with appropriate test cases that suits for solving such porous media problems is recommended and the wave propagation inside the porous media is discussed shortly.
In this project, the evolution and fundamentals of Theory of Porous Media are studied. The field ... more In this project, the evolution and fundamentals of Theory of Porous Media are studied. The field equations governing the dynamic response of a fluid-saturated elastic porous medium with intrinsically incompressible solid and fluid constituents are derived and analyzed. The results of the governing field equations are treated numerically using Standard Galerkin procedure and the Finite element method. This class of problems comes under volumetrically coupled problems due to the solid-fluid momentum interaction that involves a coupling between the momentum equations and the incompressibility constraint. In this concern, two numerical examples are considered (one-and two-dimensional wave propagation example). These examples are tested numerically using multi-field formulations feasible in porous media dynamics. The tests are carried out under different combination of approximation order of the individual unknowns with several refinement levels of mesh and different time-step sizes. Here the degree of coupling is controlled by the permeability parameter, so each test cases are carried out with both large and small permeability values. In the first numerical example, firstly the analytical solution of the fluid-saturated poroelastic medium is derived using Laplace transformation and the solutions of the unknown variables are found using MAPLE programming. Then, the solutions of different formulations,which are analyzed numerically, are compared with the analytical solution for solid displacement and pore-fluid pressure through error calculation. These error values of each test cases are plotted graphically against different time-step sizes and different mesh sizes. In the second numerical example, the propagation of solid displacement and pore-fluid pressure waves inside a porous medium is studied and the results are plotted graphically. The in-plane motion of the displacements and the pressure oscillations are compared between different formulations and polynomial degrees combinations. In conclusion, the best formulation with appropriate test cases that suits for solving such porous media problems is recommended and the wave propagation inside the porous media is discussed shortly.