Numerical methods in fluid dynamics: initial and initial boundary-value problems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | Digitally printed version, paperback re-issue |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | IX, 446 S. m |
| ISBN: | 9780521259248 9780521105521 |
Staff View
MARC
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| 245 | 1 | 0 | |a Numerical methods in fluid dynamics |b initial and initial boundary-value problems |c Gary A. Sod |
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
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| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Fluid dynamics |x Mathematics | |
| 650 | 4 | |a Numerical analysis | |
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Record in the Search Index
| _version_ | 1804138697731342336 |
|---|---|
| adam_text | Paperback
Re-issue
Here is an introduction to numerical methods for partial
differential equations
w i tli
particular reference to those that are ol
importance in fluid dynamics. The author gives a thorough and
rigorous treatment of the techniques, beginning with the classical
methods and leading to a discussion of modern developments, for
easier reading and use. many of the purely technical results and
theorems are given
separatek
from the main bock of the text.
The presentation is intended for graduate students in applied
mathematics, engineering, and the physical sciences who have a
basic knowledge of partial differential equations. Reviews ol
these topics are offered wherever appropriate and main examples
of numerical solutions are given throughout. The book also
contains an up-to-date list of references.
This book will be of great value not only to students studying
numerical methods in fluid
dv
namies,
but also to practitioners and
nonspecialists who seek a reliable introduction to the subject.
CONTENTS
Preface
Chapter I. Introduction
1.1.
Introductory example
.................................... 1
1.2.
Basic Difference Operators
.............................. 7
1.3.
Lax
s
Theorem
........................................... 12
1
.4.
The Fourier Method
...................................... 15
1.5.
References
.............................................. 20
Chapter II. Parabolic Equations
II.
К
Introduction to Parabolic Equations
..................... 21
11.
2.
Finite Difference Methods for a Single Parabolic
Equation in One Space Dimension
......................... 24
1
1.3.
Finite Difference Methods for a Single Parabolic
Equation in Several Space Dimensions
.................... 35
11.
4.
Fractional Step Methods
................................. 44
11.
5.
Alternating Direction Implicit Methods
................... 59
11.
6.
Effect of Lower Order Terms
............................. 68
11.
7.
Systems of Parabolic Equations
.......................... 73
11.
8.
Weak Stability
.......................................... 81
11.
9.
Multilevel Methods
...................................... 84
11.10.
Boundary Conditions Involving Derivatives
............... 88
11.11.
Parabolic Equations with Variable Coefficients
.......... 94
11.12.
An Example of a Nonlinear Parabolic Equation
............ 110
11.13.
Nonlinear Parabolic Equations
........................... 116
11.14.
Irregular Boundaries
.................................... 130
11.15.
Numerical Examples
...................................... 134
11.16.
References
.............................................. 141
Chapter III. Hyperbolic Equations
111.1.
Introduction to Hyperbolic Equations
.................... 143
111.
2.
The Courant-Friedrlchs-Lewy Condition
................... 151
111.3. The Algebraic Characterization of Accuracy
.............. 162
111.
4.
Finite Difference Methods with Positive Coefficients
--- 168
111.
5.
The Lax-Wendrof
f
Method
................................. 173
111.
6.
Dispersion and Dissipation
.............................. 176
111.
7.
Implicit Methods
........................................ 184
111.
8.
Systems of Hyperbolic Equations in One Space
Dimensión
............................................... 190
111.
9.
Systems of Hyperbolic Equations in Several Space
Dimensions
.............................................. 196
111.
10.
Multilevel Methods
...................................... 206
111.11.
Hyperbolic Equations with Variable Coefficients
......... 217
111.
12.
Random Choice Methods
................................... 228
111.13.
Asymptotic Error Expansion
.............................. 241
111.
14.
How Accurate Should a Finite Difference Method Be?
...... 244
111.
15.
Numerical Example
....................................... 252
111.
16.
References
.............................................. 266
vii
viii
Chapter IV. Hyperbolic Conservation Laws
IV.
1.
Introduction to Hyperbolic Conservation Laws
............ 269
IV.
2.
Conservative Finite Difference Methods
.................. 284
IV.
3.
Monotone Difference Methods
............................. 298
IV.
4.
The Godunov and Random Choice Methods
................... 321
IV.
5.
Corrective and High Resolution Methods
.................. 333
IV.
6.
Numerical Examples
...................................... 355
IV.
7.
References
.............................................. 367
Chapter V. Stability in the Presence of Boundaries
V.1. Introduction
............................................ 373
V.2. Ryabenki-Godunov Theory
................................. 375
V.3. Stability of Initial Boundary-Value Problems for
Hyperbolic Equations
.................................... 385
V.4. References
.............................................. 395
Appendices
A. The Kreiss Matrix Theorem and Its Consequences
.......... 397
B. Kreiss Stability Theorems for
Dissipât
lve
Methods
...... 403
C.
The Lax-Nirenberg Theorem and a Special Case
............ 417
D. Hyperbolic Equations with Discontinuous Initial Data
.... 427
Index
................................................... 445
|
| any_adam_object | 1 |
| author | Sod, Gary A. |
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| author_role | aut |
| author_sort | Sod, Gary A. |
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| dewey-search | 620.1064 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik |
| edition | Digitally printed version, paperback re-issue |
| format | Book |
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| spelling | Sod, Gary A. Verfasser aut Numerical methods in fluid dynamics initial and initial boundary-value problems Gary A. Sod Digitally printed version, paperback re-issue Cambridge [u.a.] Cambridge Univ. Press 2009 IX, 446 S. m txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematik Fluid dynamics Mathematics Numerical analysis Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Hydrodynamik (DE-588)4026302-2 s 1\p DE-604 Randwertproblem (DE-588)4048395-2 s 2\p DE-604 Numerische Mathematik (DE-588)4042805-9 s Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173779&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173779&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Sod, Gary A. Numerical methods in fluid dynamics initial and initial boundary-value problems Mathematik Fluid dynamics Mathematics Numerical analysis Hydrodynamik (DE-588)4026302-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd Randwertproblem (DE-588)4048395-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4026302-2 (DE-588)4128130-5 (DE-588)4077970-1 (DE-588)4048395-2 (DE-588)4042805-9 |
| title | Numerical methods in fluid dynamics initial and initial boundary-value problems |
| title_auth | Numerical methods in fluid dynamics initial and initial boundary-value problems |
| title_exact_search | Numerical methods in fluid dynamics initial and initial boundary-value problems |
| title_full | Numerical methods in fluid dynamics initial and initial boundary-value problems Gary A. Sod |
| title_fullStr | Numerical methods in fluid dynamics initial and initial boundary-value problems Gary A. Sod |
| title_full_unstemmed | Numerical methods in fluid dynamics initial and initial boundary-value problems Gary A. Sod |
| title_short | Numerical methods in fluid dynamics |
| title_sort | numerical methods in fluid dynamics initial and initial boundary value problems |
| title_sub | initial and initial boundary-value problems |
| topic | Mathematik Fluid dynamics Mathematics Numerical analysis Hydrodynamik (DE-588)4026302-2 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd Randwertproblem (DE-588)4048395-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Mathematik Fluid dynamics Mathematics Numerical analysis Hydrodynamik Numerisches Verfahren Strömungsmechanik Randwertproblem Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173779&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017173779&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sodgarya numericalmethodsinfluiddynamicsinitialandinitialboundaryvalueproblems |