Download - Finding curvature; Methods, problems and solutions

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Page 1: Finding curvature; Methods, problems and solutions

Finding curvature;Methods, problems and solutions

Mmac meetingJune 28th, 2012

Amin Ahmadi Joneidi

Page 2: Finding curvature; Methods, problems and solutions

/ Mechanical engineering

Finding curvature; Methods, problems and solutions

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Page 3: Finding curvature; Methods, problems and solutions

/ Mechanical engineering

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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/ Mechanical engineering4

H =

Physical meaning of curvature

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/ Mechanical engineering

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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