An Improved Incompressible Smoothed Particle Hydrodynamics ...

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CONTENTS 3.6 Periodic boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.7 Code structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.8 Partial conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4 ISPH Method Comparisons and Accuracy Study for ISPH_DFS 81 4.1 Taylor_Green vortices . . . . . . . . . . . . . . . . . . . . . . . . . 83 4.1.1 Case description . . . . . . . . . . . . . . . . . . . . . . . . 83 4.1.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . 84 4.2 Vortex Spin-down . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.1 Case description . . . . . . . . . . . . . . . . . . . . . . . . 91 4.2.2 FV simulations for reference . . . . . . . . . . . . . . . . . 93 4.2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . 93 4.3 Accuracy test with Taylor-Green vortices . . . . . . . . . . . . . 101 4.3.1 Relative error definition . . . . . . . . . . . . . . . . . . . 101 4.3.2 Accuracy and convergence rate of ISPH_DFS . . . . . . . 102 4.3.3 Influence of correction stage on the accuracy . . . . . . . 103 4.4 Partial conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3
CONTENTS 5 Validation by Benchmark Test Cases 110 5.1 Lid-driven cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.1.1 Case description . . . . . . . . . . . . . . . . . . . . . . . . 111 5.1.2 Simulations with STAR-CD . . . . . . . . . . . . . . . . . 113 5.1.3 Simulation results and discussion . . . . . . . . . . . . . 113 5.2 2-D laminar flow past a circular cylinder in a channel . . . . . . 119 5.2.1 Case description . . . . . . . . . . . . . . . . . . . . . . . . 119 5.2.2 Code Saturne . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.2.3 Simulation results and discussion . . . . . . . . . . . . . 122 5.3 Partial conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 6 ISPH_DFS Method in Free-Surface Flow Simulations 137 6.1 Identification of free-surface particles . . . . . . . . . . . . . . . 139 6.2 Truncated-kernel error on the free surface . . . . . . . . . . . . 139 6.3 Free-surface instability damping . . . . . . . . . . . . . . . . . . 144 6.4 Simulation of impulsive paddle . . . . . . . . . . . . . . . . . . . 152 6.4.1 Case description . . . . . . . . . . . . . . . . . . . . . . . . 152 6.4.2 Simulation parameters . . . . . . . . . . . . . . . . . . . . 152 6.4.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . 153 4
Page 1 and 2: An Improved Incompressible Smoothed
Page 3: CONTENTS 2.1.2 SPH operators . . .
Page 7 and 8: List of Figures 1.1 Density and vel
Page 9 and 10: LIST OF FIGURES 4.8 The geometry an
Page 11 and 12: LIST OF FIGURES 6.6 Geometry of dam
Page 13 and 14: List of Tables 4.1 Computing costs
Page 15 and 16: Abstract attempts to improve the ac
Page 17 and 18: Declaration No portion of the work
Page 19 and 20: Copyright 4. Further information on
Page 21 and 22: Acknowledgments Armando and other f
Page 23 and 24: Chapter 1. Introduction and Thesis
Page 41 and 42: Chapter 2 The SPH Methodology, Exis
Page 43 and 44: Chapter 2. The SPH Methodology, Exi
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Chapter 2. The SPH Methodology, Exi
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Chapter 3 The Incompressible SPH Co
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Chapter 3. The Incompressible SPH C
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3.2.3 Velocity at time n+1 u n+1 Th
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3.5 Wall boundary tests Chapter 3.
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P 0 -0.1 -0.2 -0.3 -0.4 -0.5 Chapte
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3.7 Code structure Chapter 3. The I
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Chapter 4. ISPH Method Comparisons
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Chapter 5 Validation by Benchmark T
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Chapter 5. Validation by Benchmark
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u/U 1 0.8 0.6 0.4 0.2 0 -0.2 0 0.2
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P/(ρU 2 ) 2.5 2 1.5 1 0.5 0 Chapte
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P/(ρU 2 ) 1 0.8 0.6 0.4 0.2 0 -0.2
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Y/d Y/d Y/d 4 2 0 4 2 0 4 2 0 Chapt
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y/d 6 5 4 3 2 1 0 Chapter 5. Valida
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Cd Cd 4.7 4.6 4.5 4.4 4.3 Chapter 5
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y/d y/d 5 4 3 2 1 Chapter 5. Valida
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C d max / C d min 2.85 2.8 2.75 2.7
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5.3 Partial conclusion Chapter 5. V
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Chapter 6. ISPH_DFS Method in Free-
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Relative Error 6e-05 5e-05 4e-05 3e
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Y/a Y/a Y/a 3 2 1 Chapter 6. ISPH_D
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y (m) 0.5 0.45 0.4 0.35 0.3 0.25 0.
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Chapter 7. Conclusions and Future W
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7.2 Future work and suggestions Cha
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Chapter A. The SPHysics Code In SPH
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Chapter A. The SPHysics Code SPS mo
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Chapter A. The SPHysics Code Also t
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n+1 i = rn i +∆tun i 184 Chapter
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P0 = r0 Chapter B. Linear Solvers (
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If Xi is accurate enough then quite
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Conference Publications: Chapter C.
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BIBLIOGRAPHY [7] D. L. Brown, R. Co
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BIBLIOGRAPHY [24] J. W. Dold and D.
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BIBLIOGRAPHY [39] D. Hietel, K. Ste
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BIBLIOGRAPHY [55] J. Klapp, L. D. G
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BIBLIOGRAPHY [71] J. J Monaghan. Sm
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BIBLIOGRAPHY [88] R. K. Price, The
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BIBLIOGRAPHY [105] D. Teleaga and J
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BIBLIOGRAPHY [121] SPHysics, open-s
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An Improved Incompressible Smoothed Particle Hydrodynamics ...

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