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Published byTamsyn Nicholson Modified over 9 years ago
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1 Point-implicit diffusion operator in a moving particle method (MPPM) Yao-Hsin Hwang Department of Marine Engineering National Kaohsiung Marine University
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2 Diffusion operator Time-step constraint for explicit scheme Implicit scheme: Iteration Numerically stable without iteration
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3 Features of existing particle methods SPH, MPS, FVPM…. Material particles (mass point, global mass conservation) Operators realized with randomly particle cloud
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4 Disadvantages of existing schemes Inaccurate (inconsistent) operator realization (particle smoothing) —continuity constraint Assignment of boundary condition Particle management (impractically clustered or dispersive) Computationally inefficient
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5 Essentials of MPPM (1) Inserted pressure mesh to realize pressure- related operators Background mesh and length scale Local mass conservation Particle as observation point
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6 Essentials of MPPM (2) No particle management constraint Feasible non-uniform distribution No special boundary treatment Constant and diagonally dominant coefficient matrix of pressure equation
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7 Diffusion Procedure Equation Laplacian,
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8 Explicit Operator Scheme Time-step constraint
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9 Implicit Operator Scheme Iteration required
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10 Point-implicit Operator Operator
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11 Point-implicit Operator Scheme A Scheme B
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12 Effective-Time Step Scheme A Scheme B
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13 Stability Limits Scheme A Scheme B
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14 Three-Point Analysis(1) 1. Boundary conditions: 2. Solution at 3. Results
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15 Three-Point Analysis(2) Results
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16 Pure Diffusion(1) Particle distribution
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17 Pure Diffusion(2)
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18 Pure Diffusion(3)
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19 Cavity Flow(1)
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20 Cavity Flow Re=10
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21 Cavity Flow(2)
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22 Cavity Flow(3)
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23 Cavity Flow(4)
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24 Cavity Flow(5)
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25 Backward-Facing Step Flow(1)
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26 Backward-Facing Step Flow(2)
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27 Backward-Facing Step Flow(3)
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28 Backward-Facing Step Flow(4)
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29 Backward-Facing Step Flow(5)
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30 Backward-Facing Step Flow(6)
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