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The Diffusion Hydrodynamic Model (DHM), as presented in the 1987 USGS publication, was one of the first computational fluid dynamics computational programs based on the groundwater program MODFLOW, which evolved into the control volume modeling approach. Over the following decades, others developed similar computational programs that either used the methodology and approaches presented in the DHM directly or were its extensions that included additional components and capacities. Our goal is to demonstrate that the DHM, which was developed in an age preceding computer graphics/visualization tools, is as robust as any of the popular models that are currently used. We thank the USGS for their approval and permission to use the content from the earlier USGS report.
Analysis of Hydrodynamic Models presents a concise treatment of a number of partial differential equations of hydrodynamic origin, including the incompressible Euler equations, SQG, Boussinesq, incompressible porous medium, and Oldroyd-B. The author?s approach is based on properties of the particle trajectory maps and on analysis of the back-and-forth passage between the Lagrangian and the Eulerian descriptions. This concise, unified approach brings readers up to date on current open problems. This book is intended for graduate students and junior researchers in mathematics.
Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.
This book presents a hierarchy of macroscopic models for semiconductor devices, studying three classes of models in detail: isentropic drift-diffusion equations, energy-transport models, and quantum hydrodynamic equations. The derivation of each, including physical discussions, is shown. Numerical simulations for modern semiconductor devices are performed, showing the particular features of each. The author develops modern analytical techniques, such as positive solution methods, local energy methods for free-boundary problems and entropy methods.
Overland flow modelling has been an active field of research for some years, but developments in numerical methods and computational resources have recently accelerated progress, producing models for different geometries and types of flows, such as simulations of canal and river networks. Flow in canals has traditionally been described using one-dimensional, depth-averaged, shallow water models; but a variety of simulation techniques now facilitate the management of hydrodynamic systems, providing models which incorporate complex geometry and diverse flows. Much effort has gone into elaborating canal operational rules based on decision support systems, with the dual aim of assuring water delivery and meeting flow control constraints. In natural water courses, water management problems are associated with the need to meet quality standards. Numerical modelling of advection-diffusion can be used to manage problems related to the movement of solutes in rivers and aquifers. The analysis of solute transport is used to safeguard the quality of surface and ground water and to help prevent eutrophication. Solute flow through the soil can be dynamically linked to overland flow for hydrological and agricultural applications. Advances in modelling also cast new light on sediment transport in rivers, exploring the complex dynamics of river bed erosion and deposition and assist in thee analysis of river-reservoir systems. All these issues are discussed in Numerical Modelling of Hydrodynamics for Water Resources, which will be useful to civil engineers, applied mathematicians, hydrologists, and physicists.
In many areas nutrient loadings to aquatic ecosystems have increased considerably as a result of population growth, industrial development and urbanisation. This has resulted in enhanced growth of phytoplankton, shifts in composition of the plankton community and changes in the structure of ecosystems, which are often considered to be objectionable. To help understanding these processes and to predict future conditions, a mathematical model, BLOOM, has been developed and applied since 1977. It simulates the biomass and composition of phytoplankton and macro algae in relation to the amount of nutrients, the under water light climate and grazing.
Hydrodynamics and Transport for Water Quality Modeling presents a complete overview of current methods used to describe or predict transport in aquatic systems, with special emphasis on water quality modeling. The book features detailed descriptions of each method, supported by sample applications and case studies drawn from the authors' years of experience in the field. Each chapter examines a variety of modeling approaches, from simple to complex. This unique text/reference offers a wealth of information previously unavailable from a single source. The book begins with an overview of basic principles, and an introduction to the measurement and analysis of flow. The following section focuses on rivers and streams, including model complexity and data requirements, methods for estimating mixing, hydrologic routing methods, and unsteady flow modeling. The third section considers lakes and reservoirs, and discusses stratification and temperature modeling, mixing methods, reservoir routing and water balances, and dynamic modeling using one-, two-, and three-dimensional models. The book concludes with a section on estuaries, containing topics such as origins and classification, tides, mixing methods, tidally averaged estuary models, and dynamic modeling. Over 250 figures support the text. This is a valuable guide for students and practicing modelers who do not have extensive backgrounds in fluid dynamics.
To be perfect does not mean that there is nothing to add, but rather there is nothing to take away Antoine de Saint-Exupery The drift-diffusion approximation has served for more than two decades as the cornerstone for the numerical simulation of semiconductor devices. However, the tremendous speed in the development of the semiconductor industry demands numerical simulation tools that are efficient and provide reliable results. This makes the development of a simulation tool an interdisciplinary task in which physics, numerical algorithms, and device technology merge. For the sake of an efficient code there are trade-offs between the different influencing factors. The numerical performance of a program that is highly flexible in device types and the geometries it covers certainly cannot compare with a program that is optimized for one type of device only. Very often the device is sufficiently described by a two dimensional geometry. This is the case in a MOSFET, for example, if the gate length is small compared with the gate width. In these cases the geometry reduces to the specification of a two-dimensional device. Here again the simplest geometries, which are planar or at least rectangular surfaces, will give the most efficient numerical codes. The device engineer has to decide whether this reduced description of the real device is still suitable for his purposes.