Multiphysics in Porous Materials

Abstract

"This book summarizes, defines, and contextualizes multiphysics with an emphasis on porous materials. It covers various essential aspects of multiphysics, from history, definition, and scope to mathematical theories, physical mechanisms, and numerical implementations. The emphasis on porous materials maximizes readers' understanding as these substances are abundant in nature and a common breeding ground of multiphysical phenomena, especially complicated multiphysics. Dr. Liu's lucid and easy-to-follow presentation serve as a blueprint on the use of multiphysics as a leading edge technique for computer modeling. The contents are organized to facilitate the transition from familiar, monolithic physics such as heat transfer and pore water movement to state-of-the-art applications involving multiphysics, including poroelasticity, thermohydro-mechanical processes, electrokinetics, electromagnetics, fluid dynamics, fluid structure interaction, and electromagnetomechanics. This volume serves as both a general reference and specific treatise for various scientific and engineering disciplines involving multiphysics simulation and porous materials."-- Intro; Preface; Contents; Part I: Introduction; Chapter 1: History and Future; Introduction; Multiphysics Is There; Multiphysics Is Coming; Chapter 2: What Is Multiphysics; Introduction; Definitions and Scopes; Definition 1; Definition 2; Definition 3; Definition 4; Definition in This Book; From Monolithic Physics to Multiphysics: Couplings; Physical Fields and Types of Multiphysics; Chapter 3: How to Do Multiphysics; Introduction; Mathematical Model; Discretization; Solution and Postprocessing; Chapter 4: Multiphysics in Porous Materials; Introduction; History; Applications. Chapter 5: How to Use This BookIntroduction; Organization of the Book; Suggestions to Readers; Part II: Mathematical Background; Chapter 6: Tensor and Field; Introduction; From Scalar, Vector to Tensor; Physical Field; Chapter 7: Tensor Analysis; Introduction; Notation; Vector Algebra; Vector Additions and Scalar Multiplication; Products of Vectors; Vector Calculus; Theorems; Basics of Tensor Analysis; Definition; Tensor Product; Identities and Algebra; Contraction and Inner Product; Important Identities in Vector Calculus; Operator and Order of Tensor. Special Combination of Multiple OperatorsDistributivity over Vector Addition; Product of Scalar and Vector; Scalar Triple Product; Vector Triple Product; Chapter 8: Index Notation and Tensor Notation; Introduction; Rules of Index Notation; Tensor Algebra in Index Notation; Calculus Using Index Notation; Examples of Algebraic Manipulations Using Index Notation; Chapter 9: Partial Differential Equations; Introduction; Numerical Simulation and PDEs; Classification of Partial Differential Equations; Common PDEs in Engineering Applications; Linear Equations; Nonlinear Equations. System of Partial Differential EquationsBoundary Conditions and Initial Conditions; Common Types of Boundary Conditions; Confusion About Boundary Conditions; Boundary Conditions in 3D Domains; Boundary Condition Treatments in Computer Programs; Initial Condition; Chapter 10: Numerical Solution of PDEs; Introduction; Solve PDEs with MATLAB PDE Toolbox; A PDE Implementation Tool: FlexPDE; Part III: Monolithic Physics; Chapter 11: Thermo: Heat Transfer; Introduction; General Background for Continuum Mechanics; Representative Elementary Volume; Conservation Law; Heat Transfer in Continua. Heat Transfer in Porous MaterialsHeat Capacity; Thermal Conductivity; Thermal Diffusivity; Boundary Conditions; Practice Problem; Problem Description; Solution; Appendix: MATLAB Code; Chapter 12: Hydro: Pore Water Movement; Introduction; Groundwater Movement; Mass Balance; Darcyś Law; Narrow Definition for Special Case; General Definition for Porous Materials; Derivation of Governing Equation; Water Flow in Unsaturated Zones; Derivation; Formulations; Head Based; Saturation Based; Mixed Saturated-Unsaturated Flow; Surface Flow; Practice Problem; Experiment Description.