Riemann problems and Jupyter solutions / David I. Ketcheson, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia, Randall J. LeVeque, University of Washington, Seattle, Washington, Mauricio J. del Razo, Freie Universität, Berlin, Germany.

Format:

Book

Author/Creator:

Ketcheson, David I., author.

LeVeque, Randall J., 1955- author.

Del Razo, Mauricio J., author.

Contributor:

Society for Industrial and Applied Mathematics, publisher.

Series:

Fundamentals of algorithms ; 16.

Fundamentals of algorithms ; 16

Language:

English

Subjects (All):

Riemann-Hilbert problems.

Differential equations, Hyperbolic.

Physical Description:

1 online resource (xii, 166 pages) : illustrations.

Place of Publication:

Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), [2020]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

This book addresses an important class of mathematical problems--the Riemann problem--for first-order hyperbolic partial differential equations (PDEs), which arise when modeling wave propagation in applications such as fluid dynamics, traffic flow, acoustics, and elasticity. The solution of the Riemann problem captures essential information about these models and is the key ingredient in modern numerical methods for their solution. This book covers the fundamental ideas related to classical Riemann solutions, including their special structure and the types of waves that arise, as well as the ideas behind fast approximate solvers for the Riemann problem. The emphasis is on the general ideas, but each chapter delves into a particular application. Riemann Problems and Jupyter Solutions is available in electronic form as a collection of Jupyter notebooks that contain executable computer code and interactive figures and animations, allowing readers to grasp how the concepts presented are affected by important parameters and to experiment by varying those parameters themselves; is the only interactive book focused entirely on the Riemann problem; and develops each concept in the context of a specific physical application, helping readers apply physical intuition in learning mathematical concepts.

Contents:

1. Introduction

2. Advection

3. Acoustics

4. Burgers' equation

5. Traffic flow. The Lighthill-Whitham-Richards model

6. Nonconvex scalar conservation laws

7. The shallow water equations

8. Shallow water equations with a tracer

9. The Euler equations of gas dynamics

10. Introduction to approximate Riemann solvers

11. An approximate solver for Burgers' equation

12. Approximate solvers for the shallow water equations

13. Approximate solvers for the Euler equations of gas dynamics

14. Finite volume discretizations with approximate Riemann solvers.

Notes:

Includes bibliographical references and index.

Description based on title page of print version.

ISBN:

1-61197-621-9

OCLC:

1150854022

Publisher Number:

FA16 SIAM