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immiscible LB

immiscible LB



23 Jul 2009 (Updated )

Implements Immiscible Lattice Boltzmann (ILB, D2Q9) method for two phase flows

[H K]=HK(Z)
% Function Name : HK
% Author    Alireza Bossaghzadeh
% PURPOSE:  The Code calculate the Mean and Gaussian Curvature according to the method described in
% Modern Differential Geometry of Curves and Surfaces with Mathematica.2nd ed, 1997 (p. 377).

% The method Used in the Code:
% If x:U->R^3 is a regular patch, then the mean curvature is given by
%           H = (eG-2fF+gE)/(2(EG-F^2)),	
%           G = (eg-f^2)   /(EG-F^2)
% where E, F, and G are coefficients of the first fundamental form and
% e, f, and g are coefficients of the second fundamental form 
% For more information see Links Below

% Function Variables:
% Input             I   mesh contain depth values
% outputs           H   Contain Mean Curvature of surface
%                   K   Contain Gaussian Curvature of surface
% Example           [H K]=HK(I);

% In the case of any problem you can call me by 

% Version:    1.00       Published: 2008 June 07

%This Code was written By Alireza Bossaghzadeh.
%In the case of any problem you can contact me By

function [H K]=HK(Z)

% Calculate base parameters
    Zx  =gradient(Z);
    Zxx =gradient(Zx);
    Zy  =gradient(Z')';
    Zyy =gradient(Zy')';
    Zxy =gradient(Zx')';

%Calculate First Fundamental Form coefficients
%Calculate First Fundamental Form coefficients
% Calculate Mean Curvature    

%This code also can be used
%     H=(1+Zx.^2).*Zyy-2.*Zx.*Zy.*Zxy+(1+Zy.^2).*Zxx;
%     H=-H./(2.*(1+Zx.^2+Zy.^2).^(3/2));

% Calculate Gaussian Curvature

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