Homotopy-Based Methods in Water Engineering

Most complex physical phenomena can be described by nonlinear equations, specifically, differential equations. In water engineering, nonlinear differential equations play a vital role in modeling physical processes. Analytical solutions to strong nonlinear problems are not easily tractable, and existing techniques are problem-specific and applicable for specific types of equations. Exploring the concept of homotopy from topology, different kinds of homotopy-based methods have been proposed for analytically solving nonlinear differential equations, given by approximate series solutions. Homotopy-Based Methods in Water Engineering attempts to present the wide applicability of these methods to water engineering problems. It solves all kinds of nonlinear equations, namely algebraic/transcendental equations, ordinary differential equations (ODEs), systems of ODEs, partial differential equations (PDEs), systems of PDEs, and integro-differential equations using the homotopy-based methods. The content of the book deals with some selected problems of hydraulics of open-channel flow (with or without sediment transport), groundwater hydrology, surface-water hydrology, general Burger's equation, and water quality. Features: - Provides analytical treatments to some key problems in water engineering - Describes the applicability of homotopy-based methods for solving nonlinear equations, particularly differential equations - Compares different approaches in dealing with issues of nonlinearity

Manotosh Kumbhakar is a Postdoctoral Researcher at National Taiwan University, Tawan. Previously, he was a Postdoctoral Research Associate at Texas A&M University, USA, from 2020-2021. He specializes in entropy theory, mechanics of sediment transport, and semi-analytical methods. Dr. Manotosh has published several papers in reputed international journals. Vijay P. Singh, Ph.D., D.Sc., D. Eng. (Hon.), Ph.D. (Hon..), P.E., P.H., Hon. D. WRE, Dist.M. ASCE, NAE, is a Distinguished Professor, a Regents Professor, and Caroline & William N. Lehrer Distinguished Chair in Water Engineering in Department of Biological and Agricultural Engineering and Zachry Department of Civil & Environmental Engineering at Texas A&M University. He specializes in surface-water hydrology, groundwater hydrology, hydraulics, irrigation engineering, environmental and water resources engineering, entropy theory, and copula theory. Professor Singh has published extensively and has received 110 national and international awards, including three honorary doctorates. He is a member of National Academy of Engineering, and a fellow or member of 12 international engineering/science academies.

Part One: Introduction. 1. Introduction. 2. Basic Concepts. Part Two: Algebraic/Transcendental Equations. 3. Numerical Solution for Colebrook Equation. Part Three: Ordinary Differential Equations (ODEs) (Single and System). 4. Velocity Distribution in Smooth Uniform Open Channel Flow. 5. Sediment Concentration Distribution in Open-Channel Flow. 6. Richards Equation Under Gravity-Driven Infiltration and Constant Rainfall Intensity. 7. Error Equation for Unsteady Uniform Flow. 8. Spatially Varied Flow Equations. 9. Modeling of Nonlinear Reservoir. 10. Nonlinear Muskingum Method for Flood Routing. 11. Velocity and Sediment Concentration Distribution in Open Channel Flow. Part Four: Partial Differential Equations (PDES) (Single and System). 12. Unsteady Confined Radial Ground-Water Flow Equation. 13. Series Solutions for Burger's Equations. 14. Diffusive Wave Flood Routing Problem with Lateral Inflow. 15. Kinematic Wave Equation. 16. Multispecies Convection-Dispersion Transport Equation with Variable Parameters. Part Five: Integro-Differential Equations. 17. Absorption Equation in Unsaturated Soil.