Synopsis
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.
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Construction of Solutions for Two Dimensional Riemann Problems
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Paperback. Condition: New. 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. print-on-demand item. Seller Inventory # 9781333652050_0
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Construction of Solutions for Two Dimensional Riemann Problems (Classic Reprint)
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333652050
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Construction of Solutions for Two Dimensional Riemann Problems (Classic Reprint)
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333652050
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