This book presents a detailed account of flow simulation in shallow water regions using the finite element method. Shallow water equations are widely employed to model water behavior in oceans, coastal waters, estuaries, rivers, and lakes, and also provide a basis for the analysis of fluid flows in an adiabatic state. The computational approaches discussed in this volume are therefore applicable beyond shallow water problems and extend to a broader class of continuum flow analyses.

The book focuses on finite element formulations for linear waves and shallow water flows. The early chapters introduce the theoretical background through the mild slope equation and the Helmholtz equation, with particular attention to numerical treatments of unbounded domains. These are followed by derivations of the shallow water and Boussinesq equations and an introductory presentation of finite element methods for their analysis. More advanced topics are addressed in later chapters, which survey recent developments such as bubble function interpolations, mixed and discontinuous interpolation methods, as well as formulations in curvilinear and spherical coordinate systems. The final part of the book extends the discussion to analyses involving uncertainty, introducing the Kalman filter finite element method to reconcile numerical simulations with observational data.

With illustrative numerical examples throughout, this book offers a coherent treatment of theoretical foundations and numerical methods. It serves as a useful reference for researchers and graduate students engaged in computational fluid dynamics, coastal and hydraulic engineering, and related fields concerned with the numerical simulation of shallow water flows.

Mutsuto Kawahara is an emeritus professor at Chuo University. He received his Ph.D. from the Department of Civil Engineering at Waseda University in 1973. He started his academic career at the Department of Civil Engineering, Chuo University as a lecturer in 1971. He was promoted to an associate professor and professor there in 1974 and 1983, respectively, and retired in 2013. He was awarded the prizes from the Asian Pacific Association for Computational Mechanics in 2006, the International Association for Computational Mechanics in 2008, and furthermore the Order of the Sacred Treasure, Gold Rays with Neck Ribbon. He had been an associate editor of the International Journal of Computational Fluid Dynamics.