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E-grāmata: Smoothed Particle Hydrodynamics: Fundamentals and Basic Applications in Continuum Mechanics

  • Formāts: PDF+DRM
  • Izdošanas datums: 30-Nov-2018
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030007737
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Smoothed Particle Hydrodynamics: Fundamentals and Basic Applications in Continuum MechanicsPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 30-Nov-2018
  • Izdevniecība: Springer Nature Switzerland AG
  • Valoda: eng
  • ISBN-13: 9783030007737
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This book is based on results obtained over a decade of study and research. It questions the use of dynamic molecular models in the continuum scale providing alternative solutions to open problems in the literature. It provides a physical-mathematical understanding of the differential equations that govern fluid flow and energy transport, serving as a reference to the application of Smoothed Particle Hydrodynamics in continuum fluid mechanics and transport phenomena. The physical-mathematical modelling of the problems in the continuum scale and the employment of the SPH method for solving the equations are presented. Examples of applications in continuum fluid mechanics with numerical results and discussions are also provided. This literature defends the concepts of continuum mechanics and the application of boundary treatment techniques that do not violate the laws of physics. 
1 Introduction 1(10)
1.1 General
1(2)
1.2 Scientific Method of Problem-Solving
3(2)
1.3 Objective
5(1)
1.4 Presentation of the Remaining
Chapters
5(1)
References
6(5)
2 Physical-Mathematical Modelling 11(6)
2.1 The Continuum Hyphothesis
11(1)
2.2 Physical Laws of Conservation
12(1)
2.3 Pressure Modelling
13(2)
2.3.1 Equation of State for Dynamic Pressure
13(1)
2.3.2 Modified Pressure
14(1)
2.4 Specific Internal Energy Modelling
15(1)
References
15(2)
3 Smoothed Particle Hydrodynamics Method 17(50)
3.1 Fundamentals
17(2)
3.2 Discretization of the Continuum Domain
19(24)
3.2.1 Approximation of the Divergent of a Vectorial Function
20(2)
3.2.2 Approximation of the Gradient of a Scalar Function
22(2)
3.2.3 Approximation of the Laplacian
24(1)
3.2.4 SPH Approximations to the Conservation Equations
25(1)
3.2.5 Errors in SPH Approximations
26(1)
3.2.6 Smoothing Functions
26(2)
3.2.7 Neighbouring Particles Search
28(1)
3.2.8 Treatment of the Free Surface
29(6)
3.2.9 Treatment of the Interfaces
35(2)
3.2.10 Turbulence
37(2)
3.2.11 Variable Smoothing Length
39(1)
3.2.12 Numerical Aspects and Corrections
40(3)
3.3 Temporal Integration Methods
43(3)
3.3.1 Euler's Integration Method
44(1)
3.3.2 Leapfrog Method
45(1)
3.3.3 Predictor-Corrector
45(1)
3.4 Consistency
46(7)
3.4.1 Restoration of the Consistency
48(5)
3.5 Boundary Treatment Techniques
53(9)
3.5.1 Fictitious Particles and Artificial Repulsive Forces
54(2)
3.5.2 Dynamic Boundary Conditions
56(1)
3.5.3 Reflective Boundary Conditions
56(4)
3.5.4 Open Periodic Boundary Conditions
60(1)
3.5.5 Additional Remarks
61(1)
References
62(5)
4 Applications in Continuum Fluid Mechanics and Transport Phenomena 67(34)
4.1 Procedure Employed in Problem-Solving
67(1)
4.2 Heat Diffusion in a Homogeneous Flat Plate
68(10)
4.2.1 Physical-Mathematical Modelling
68(3)
4.2.2 Numerical Simulations
71(5)
4.2.3 Comments
76(2)
4.3 Still Liquid Inside an Immobile Reservoir
78(6)
4.3.1 Physical-Mathematical Modelling
78(2)
4.3.2 Numerical Simulations
80(3)
4.3.3 Comments
83(1)
4.4 Dam Breaking Over a Dry Bed
84(5)
4.4.1 Physical-Mathematical Modelling
84(1)
4.4.2 Numerical Simulations
85(3)
4.4.3 Comments
88(1)
4.5 Oil Spreading on a Calm Sea
89(9)
4.5.1 Motivation
89(2)
4.5.2 Physical-Mathematical Modelling
91(1)
4.5.3 Numerical Simulations
92(4)
4.5.4 Results and Discussions
96(2)
4.6 Concluding Remarks
98(1)
References
99(2)
Computer Code 101(4)
Conclusion 105(2)
Appendix A: Smoothing Functions, Derivatives and Normalization Constants 107(8)
Appendix B: Deduction of the SPH Laplacian Operator 115(6)
FORTRAN Source Files 121(22)
References 143(2)
Index 145
Carlos Alberto Dutra Fraga Filho is Professor of Engineering at Federal Institute of Espķrito Santo, Brazil, and leader of the research group "Development, Implementation and Application of Computational Tools for the Solution of Problems in Engineering" at the same institution. He has experience in Mechanical and Environmental Engineering, with emphasis on Computational Fluid Dynamics, working mainly in the following areas: Lagrangian modelling and Smoothed Particle Hydrodynamics (SPH) Method, Fluid Mechanics and Transport Phenomena. 
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