Finding curvature; Methods, problems and solutions
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Transcript of Finding curvature; Methods, problems and solutions
Finding curvature;Methods, problems and solutions
Mmac meetingJune 28th, 2012
Amin Ahmadi Joneidi
/ Mechanical engineering
Finding curvature; Methods, problems and solutions
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Energy and force terms
Ca, Capillary number
H, Mean curvature
K, Gaussian curvature
ζ, Lagrangian multiplier
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Stress jump across the membrane of the drop
Stress jump across the membrane of the RBC
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H =
Physical meaning of curvature
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Interface definition
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H = 2
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Curvature finding
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Contour integration method
Loewenberg and Hinch (1996)
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n = 6 El. Number = 720
H =
2.2838 For 12 special nodes
For remained nodes
Validation
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n = 10 El. Number = 2000
H =
2.2891 For 12 special nodes
For remained nodes
Validation
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n = 12 El. Number = 2880
H =
2.2899 For 12 special nodes
For remained nodes
Validation
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Drop in shear flow
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Switch from water to blood
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Curvature finding
Parabola fitting method - Zinchenko et al. (1997)
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Curvature in ellipsoid
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Curvature finding using contour integration method
Curvature finding using Parabola fitting method
Node number Numerical curvature Analytical curvatureNode 300 1.659048 1.659027Node 1200 2.329654 2.324415Node 1424 1.640974 1.636053******** ******** ********Node 1 1.8723 1.6341Node 16 3.2547 2.8442Node 136 1.9424 1.6954
Node number Numerical curvature Analytical curvatureNode 300 1.662357 1.659027Node 1200 2.328483 2.324415Node 1424 1.637966 1.636053******** ******** ********Node 1 1.6357 1.6341Node 16 2.8475 2.8442Node 136 1.6971 1.6954
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Mesh destruction
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Seek the problem
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