DIFFUSION IN DEFORMING POROUS MEDIA R.E. SHOWALTER Abstract. We report on some recent progress in the mathematical theory of nonlinear fluid transport and poro-mechanics, specifically, the design, analysis and application of mathematical models for the flow of fluids driven by the cou- pled pressure and stress distributions within a deforming heterogeneous porous structure. The goal of this work is to develop a set of mathematical models of coupled flow and deformation processes as a basis for fundamental research on the theoretical and numerical modeling and simulation of flow in deforming heterogeneous porous media. Contents 1. Introduction 2 1.1. Applications 2 1.2. Objectives 4 2. Recent Results 5 2.1. The Linear Quasi-Static Case 5 2.2. Composite Deformable Porous Media 6 2.3. The Deforming Dam 7 3. Current Progress 9 3.1. Visco-Plastic Media 9 3.2. Multi-Scale Problems 11 4. Conclusion 14 References 15 Date : October 30, 2002. 2000 Mathematics Subject Classification. Primary 74F10, 76S05, 74C05; Secondary 35K90, 35K65, 35F25. Key words and phrases. Poroelasticity, poro-plasticity, infiltration, degenerate parabolic systems. This material is based in part upon work supported by the Texas Advanced Research Program. 1
DIFFUSION IN DEFORMING POROUS MEDIA
May 16, 2023
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