Construction of Solutions for Two Dimensional Riemann Problems
Language: English
Published by Forgotten Books, 2024
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
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Condition: New
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Print on Demand. This book covers the foundational knowledge of piecewise solutions to two-dimensional Riemann problems. These are linear differential equations which form from a jump in value within a continuous function, specifically equations that contain only one inflection point. The author begins by explaining the reduction of generalized Riemann problems to one-dimensional Riemann problems and the conditions under which solutions to such equations are piecewise smooth. The bulk of the book focuses on the identification of general two-dimensional non-linear waves as they relate to piecewise smooth solutions to the two-dimensional Riemann problem for the case where the scalar input functions f and g have only one inflection point and differ by a multiplicative constant. The author classifies these waves and discusses the entropy condition as it applies to the jump points and irregular points that arise. This book then goes on to demonstrate a construction method for generating entropy-obeying solutions from the identified non-linear waves. The solution for a function with no inflection points is presented, along with an example of a function with a single inflection point. The book concludes with an application of these two-dimensional Riemann problems to the study of two-phase flow in porous media, specifically the interaction of water and oil banks in oil reservoirs. The author explains how the dynamics of these interactions can be approximated by solving the Riemann problem for the governing equations of incompressible two-phase flow. This book presents a rigorous and in-depth exploration of two-dimensional Riemann problems and their solutions, making it an essential resource for researchers and professionals working in applied mathematics, fluid dynamics, and related fields. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781333652050_0
- Title
- Construction of Solutions for Two Dimensional Riemann Problems
- Author
- W. Brent Lindquist
- Publisher
- Forgotten Books
- Publication year
- 2024
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1333652054
- ISBN 13
- 9781333652050
- Seller catalogs
- Calculus
In 52, the two dimensional nonlinear waves are described for the class of problems f, fz. In 53 a method for explicitly constructing the 2-dimensional solutions in this class from the nonlinear waves is described. Complete solutions for 2-dimensional Riemann problems for representative forms of the function f are given. Solutions to the problem of water/oil bank interactions in two phase, incompressible, gravity free, flow in reservoirs can be obtained from the study of these 2-dimensional Riemann problems. The results for this physical problem are presented in 54. Conclusions and conjectures for the solutions to 2-dimensional Riemann problems for the casef having more than one inflection points orf1 at [2 are presented in 55.
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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
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