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Numerical Methods for Eulerian and Lagrangian Conservation Laws 1st ed. 2017 [Pehme köide]

  • Formaat: Paperback / softback, 349 pages, kõrgus x laius: 240x168 mm, kaal: 6156 g, 3 Illustrations, color; 100 Illustrations, black and white; XVII, 349 p. 103 illus., 3 illus. in color., 1 Paperback / softback
  • Sari: Frontiers in Mathematics
  • Ilmumisaeg: 20-Jul-2017
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3319503545
  • ISBN-13: 9783319503547
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Numerical Methods for Eulerian and Lagrangian Conservation Laws 1st ed. 2017Suurem pilt
  • Formaat: Paperback / softback, 349 pages, kõrgus x laius: 240x168 mm, kaal: 6156 g, 3 Illustrations, color; 100 Illustrations, black and white; XVII, 349 p. 103 illus., 3 illus. in color., 1 Paperback / softback
  • Sari: Frontiers in Mathematics
  • Ilmumisaeg: 20-Jul-2017
  • Kirjastus: Birkhauser Verlag AG
  • ISBN-10: 3319503545
  • ISBN-13: 9783319503547
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319503547.html
Märksõnad:

This book focuses on the interplay between Eulerian and Lagrangian conservation laws for systems that admit physical motivation and originate from continuum mechanics. Ultimately, it highlights what is specific to and beneficial in the Lagrangian approach and its numerical methods. The two first chapters present a selection of well-known features of conservation laws and prepare readers for the subsequent chapters, which are dedicated to the analysis and discretization of Lagrangian systems.

The text is at the frontier of applied mathematics and scientific computing and appeals to students and researchers interested in Lagrangian-based computational fluid dynamics. It also serves as an introduction to the recent corner-based Lagrangian finite volume techniques.

Arvustused

The book is very fluently written and easily digested. Numerous illustrations are given to demonstrate the efficiency of the numerical methods. I strongly recommend this book, not only to the mathematically inclined CFD practitioner, but also as illuminating supplementary material for students learning the numerical analysis and the foundations of hyperbolic conservation laws. (Tore Flåtten, Mathematical Reviews, August, 2018)

Preface v
List of Figures
xiii
List of Tables
xvii
1 Models
1(40)
1.1 Balance law
1(10)
1.1.1 Traffic flow
3(1)
1.1.2 Shallow water
4(4)
1.1.3 Compressible gas dynamics
8(3)
1.1.4 Canonical form of a system of conservation laws
11(1)
1.2 Lagrangian coordinates
11(9)
1.2.1 General change of coordinates in balance laws
12(3)
1.2.2 Lagrangian gas dynamics in dimension d = 1
15(2)
1.2.3 Lagrangian gas dynamics in dimension d = 2
17(2)
1.2.4 Hui's formulation
19(1)
1.2.5 Lagrangian gas dynamics in dimension d = 3
19(1)
1.3 Frame invariance
20(4)
1.3.1 Naive method
21(2)
1.3.2 A general method
23(1)
1.4 Linear stability and hyperbolicity
24(14)
1.4.1 Classification in dimension d = 1
25(3)
1.4.2 A useful property
28(1)
1.4.3 Generalization to dimension d ≥ 2
29(1)
1.4.4 Examples
30(8)
1.5 Exercises
38(2)
1.6 Bibliographic notes
40(1)
2 Scalar conservation laws
41(52)
2.1 Strong solutions
42(4)
2.2 Weak solutions
46(4)
2.3 Entropy weak solutions
50(11)
2.3.1 En tropic discontinuities
54(2)
2.3.2 Shocks and contact discontinuities
56(2)
2.3.3 Rarefaction fans
58(1)
2.3.4 The entropic solution of the Rieniann problem
59(2)
2.4 Peculiarities of Lagrangian traffic flow
61(6)
2.4.1 Application and physical interpretation
63(4)
2.5 Numerical computation of entropy weak solutions
67(16)
2.5.1 Notion of a conservative finite volume scheme
67(3)
2.5.2 Finite volume scheme
70(1)
2.5.3 Construction of the flux using the method of characteristics
71(5)
2.5.4 Definition of a generic flux
76(3)
2.5.5 Convergence
79(3)
2.5.6 Scheme optimization
82(1)
2.6 More schemes for the traffic flow equation
83(6)
2.6.1 Numerical illustrations
85(4)
2.7 Exercises
89(2)
2.8 Bibliographic notes
91(2)
3 Systems and Lagrangian systems
93(72)
3.1 Generalities
94(9)
3.1.1 The Godunov theorem
97(4)
3.1.2 Entropy weak solutions
101(2)
3.2 Lagrangian systems in dimension d = 1
103(12)
3.2.1 Systems with a zero entropy flux
104(7)
3.2.2 A more general Lagrangian structure
111(4)
3.3 Examples of Lagrangian systems
115(15)
3.3.1 Ideal MHD
115(4)
3.3.2 Compressible elasticity
119(4)
3.3.3 Landau model for superfluid helium
123(3)
3.3.4 A multiphase model
126(4)
3.4 Self-similar solutions and the solution of the Riemann problem
130(17)
3.4.1 Rarefaction fans
131(2)
3.4.2 Entropy discontinuities
133(7)
3.4.3 Lax theorem in the space U
140(4)
3.4.4 A Lagrangian Lax theorem in the space W
144(3)
3.5 Multidimensional Lagrangian systems
147(5)
3.6 More on compressible gas dynamics
152(6)
3.6.1 Rarefaction fans
153(1)
3.6.2 Discontinuities
154(4)
3.6.3 The Riemann problem for gas dynamics
158(1)
3.7 Exercises
158(5)
3.8 Bibliographic notes
163(2)
4 Numerical discretization
165(98)
4.1 Compressible gas dynamics
165(28)
4.1.1 Principle of a Lagrange+remap scheme in one dimension
167(1)
4.1.2 Principle of an entropy Lagrangian solver
168(1)
4.1.3 Entropy Lagrangian solver based on matrix splitting
169(5)
4.1.4 An optimal splitting for fluid dynamics
174(5)
4.1.5 Moving grid
179(1)
4.1.6 Remapping
180(1)
4.1.7 Eulerian formulation of a Lagrange+remap scheme
181(3)
4.1.8 Boundary conditions
184(1)
4.1.9 A simple numerical result
185(1)
4.1.10 Pure Lagrange and ALE methods in one dimension
185(8)
4.2 Linearized Riemann solvers and matrix splittings
193(18)
4.2.1 Solution of the Lagrangian linearized Riemann problem
197(1)
4.2.2 One-state solvers
198(1)
4.2.3 Two-state solvers
199(8)
4.2.4 Optimality of the two-state solver
207(4)
4.3 Extension to multidimensional Lagrangian systems
211(12)
4.3.1 A generic discrete entropy inequality
211(4)
4.3.2 Cylindrical and spherical gas dynamics
215(1)
4.3.3 Lagrange+remap MHD in dimension d > 1
216(7)
4.4 Lagrangian gas dynamics in dimension d = 2
223(32)
4.4.1 Elementary considerations on moving meshes
223(2)
4.4.2 Some notation
225(1)
4.4.3 Compatibility with Piola identities
226(2)
4.4.4 Compatibility with Hui's formulation
228(1)
4.4.5 First attempt and geometrical obstruction
228(3)
4.4.6 Solving the geometrical obstruction: GLACE and EUCCLHYD
231(10)
4.4.7 Comparison with a scheme on a staggered mesh
241(4)
4.4.8 Well-balanced hydrostatic cell-centered Lagrangian schemes
245(7)
4.4.9 Mesh considerations and numerical examples
252(3)
4.5 Calculation of Lagrangian multi-material problems
255(4)
4.6 Exercises
259(1)
4.7 Bibliographic notes
260(3)
5 Starting from the mesh
263(68)
5.1 Axiomatization of mesh features
264(14)
5.1.1 Planar geometries
265(3)
5.1.2 The reference cell method
268(6)
5.1.3 Nodal control volumes
274(2)
5.1.4 Axisymmetric geometry
276(2)
5.2 Cell-centered Lagrangian schemes
278(9)
5.2.1 Construction of the scheme
279(4)
5.2.2 Time discretization and extensions
283(4)
5.3 Stability of the mesh for simplexes
287(3)
5.4 Weak consistency of the gradient and divergence operators
290(7)
5.4.1 Additional inequalities
291(1)
5.4.2 Gradient
292(4)
5.4.3 Divergence
296(1)
5.5 Weak consistency of Lagrangian schemes
297(5)
5.5.1 Notation
298(1)
5.5.2 The density equation
299(2)
5.5.3 The momentum equation
301(1)
5.5.4 The energy equation
302(1)
5.5.5 The entropy inequality
302(1)
5.6 Stabilization with subzonal entropies
302(13)
5.6.1 Lagrangian properties of volume fractions
305(3)
5.6.2 Building a scheme with subzonal entropies
308(3)
5.6.3 Consistency of subzonal entropies
311(1)
5.6.4 Numerical illustration
312(3)
5.7 Constraints and quadratic formulation of fluxes
315(12)
5.7.1 Quadratic functionals
315(3)
5.7.2 Application to contact problems
318(5)
5.7.3 Non-conformal meshes, hanging nodes and internal constraints
323(4)
5.8 Bibliographic notes
327(4)
Bibliography 331(16)
Subject Index 347