Finding curvature; Methods, problems and solutions

Post on 08-Feb-2016

44 views 0 download

description

Finding curvature; Methods, problems and solutions. Mmac meeting June 28th, 2012 Amin Ahmadi Joneidi. Finding curvature; Methods, problems and solutions. Energy and force terms. Ca, Capillary number. H, Mean curvature. K, Gaussian curvature. ζ , Lagrangian multiplier. - PowerPoint PPT Presentation

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

2

/ Mechanical engineering

Energy and force terms

Ca, Capillary number

H, Mean curvature

K, Gaussian curvature

ζ, Lagrangian multiplier

PAGE 3

Stress jump across the membrane of the drop

Stress jump across the membrane of the RBC

/ Mechanical engineering4

H =

Physical meaning of curvature

/ Mechanical engineering

Interface definition

PAGE 5

H = 2

/ Mechanical engineering

Curvature finding

PAGE 6

Contour integration method

Loewenberg and Hinch (1996)

/ Mechanical engineering7

n = 6 El. Number = 720

H =

2.2838 For 12 special nodes

For remained nodes

Validation

/ Mechanical engineering8

n = 10 El. Number = 2000

H =

2.2891 For 12 special nodes

For remained nodes

Validation

/ Mechanical engineering9

n = 12 El. Number = 2880

H =

2.2899 For 12 special nodes

For remained nodes

Validation

/ Mechanical engineering10

Drop in shear flow

/ Mechanical engineering11

Switch from water to blood

/ Mechanical engineering

Curvature finding

Parabola fitting method - Zinchenko et al. (1997)

PAGE 12

/ Mechanical engineering13

Curvature in ellipsoid

/ Mechanical engineering14

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

/ Mechanical engineering15

/ Mechanical engineering

Mesh destruction

PAGE 16

/ Mechanical engineering

Seek the problem

PAGE 17

/ Mechanical engineering18