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Copy pathVectorE_time_2nd_order_omega.m
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VectorE_time_2nd_order_omega.m
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function [ex,ey,ez]= VectorE_time_2nd_order_omega(x,y,z,u, v, w, ox,oy,oz,oxt,oyt,ozt,tau)
%(x,y,z,us,vs,ws,ox,oy,oz,oxt,oyt,ozt,tau);
% This function computes the right hand side of vorticity transport
% equation. It is based on the central differnces scheme amd has the second
% order of approximation.
global add nmr num div beta alpha nmr0 fle form gau hx hy hz;
dox= zeros(x,y,z);
doy= zeros(x,y,z);
doz= zeros(x,y,z);
oxx= zeros(x,y,z);
oxy= zeros(x,y,z);
oxz= zeros(x,y,z);
oyx= zeros(x,y,z);
oyy= zeros(x,y,z);
oyz= zeros(x,y,z);
ozx= zeros(x,y,z);
ozy= zeros(x,y,z);
ozz= zeros(x,y,z);
ux= zeros(x,y,z);
uy= zeros(x,y,z);
uz= zeros(x,y,z);
vx= zeros(x,y,z);
vy= zeros(x,y,z);
vz= zeros(x,y,z);
wx= zeros(x,y,z);
wy= zeros(x,y,z);
wz= zeros(x,y,z);
%------------------------------------omega---------------------------------
for i=3:x-2
for j=3:y-2
for k=3:z-2
dox(i,j,k)=(ox(i,j,k)-oxt(i,j,k))/tau;
doy(i,j,k)=(oy(i,j,k)-oyt(i,j,k))/tau;
doz(i,j,k)=(oz(i,j,k)-ozt(i,j,k))/tau;
end
end
end
[dox] = boundary_linear(dox,dox);
[doy] = boundary_linear(doy,doy);
[doz] = boundary_linear(doz,doz);
for i = 1:2
[dox]=interpolate_your_neighbour(dox);
[doy]=interpolate_your_neighbour(doy);
[doz]=interpolate_your_neighbour(doz);
end
%_______________________________________________Skorosti__________
for i=2:x-1
for j=2:y-1
for k=2:z-1
if (i>1 && i<x)
oxx(i,j,k)= (ox(i+1,j,k)-ox(i-1,j,k))/(2*hx);
oyx(i,j,k)= (oy(i+1,j,k)-oy(i-1,j,k))/(2*hx);
ozx(i,j,k)= (oz(i+1,j,k)-oz(i-1,j,k))/(2*hx);
ux(i,j,k)= (u(i+1,j,k)-u(i-1,j,k))/(2*hx);
vx(i,j,k)= (v(i+1,j,k)-v(i-1,j,k))/(2*hx);
wx(i,j,k)= (w(i+1,j,k)-w(i-1,j,k))/(2*hx);
end
if (j>1 && j<y)
oxy(i,j,k)= (ox(i,j+1,k)-ox(i,j-1,k))/(2*hy);
oyy(i,j,k)= (oy(i,j+1,k)-oy(i,j-1,k))/(2*hy);
ozy(i,j,k)= (oz(i,j+1,k)-oz(i,j-1,k))/(2*hy);
uy(i,j,k)= (u(i,j+1,k)-u(i,j-1,k))/(2*hy);
vy(i,j,k)= (v(i,j+1,k)-v(i,j-1,k))/(2*hy);
wy(i,j,k)= (w(i,j+1,k)-w(i,j-1,k))/(2*hy);
end
if (k>1 && k<z)
oxz(i,j,k)= (ox(i,j,k+1)-ox(i,j,k-1))/(2*hz);
oyz(i,j,k)= (oy(i,j,k+1)-oy(i,j,k-1))/(2*hz);
ozz(i,j,k)= (oz(i,j,k+1)-oz(i,j,k-1))/(2*hz);
uz(i,j,k)= (u(i,j,k+1)-u(i,j,k-1))/(2*hz);
vz(i,j,k)= (v(i,j,k+1)-v(i,j,k-1))/(2*hz);
wz(i,j,k)= (w(i,j,k+1)-w(i,j,k-1))/(2*hz);
end
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
%--------------------------------------------------------------------------
end
end
end
%--------------------- Boundaries --------------------------------------
ex = zeros(x,y,z);
ey = zeros(x,y,z);
ez = zeros(x,y,z);
ex = zeros(x,y,z);
ey = zeros(x,y,z);
ez = zeros(x,y,z);
ex(2:x-1,2:y-1,2:z-1)= dox(2:x-1,2:y-1,2:z-1);
ey(2:x-1,2:y-1,2:z-1)= doy(2:x-1,2:y-1,2:z-1);
ez(2:x-1,2:y-1,2:z-1)= doz(2:x-1,2:y-1,2:z-1);
%----------------------------------------------Vector E
for i=2:x-1
for j=2:y-1
for k=2:z-1
unw= u(i,j,k)*oxx(i,j,k) + v(i,j,k)*oxy(i,j,k) + w(i,j,k)*oxz(i,j,k);
wnu= ox(i,j,k)*ux(i,j,k) + oy(i,j,k)*uy(i,j,k) + oz(i,j,k)*uz(i,j,k);
ex(i,j,k) = ex(i,j,k) - 1*(unw + wnu);
%--
vnw= u(i,j,k)*oyx(i,j,k) + v(i,j,k)*oyy(i,j,k) + w(i,j,k)*oyz(i,j,k);
wnv= ox(i,j,k)*vx(i,j,k) + oy(i,j,k)*vy(i,j,k) + oz(i,j,k)*vz(i,j,k);
ey(i,j,k) = ey(i,j,k)+ (vnw- wnv);
%-----
dnw= u(i,j,k)*ozx(i,j,k) + v(i,j,k)*ozy(i,j,k) + w(i,j,k)*ozz(i,j,k);
wnd= ox(i,j,k)*wx(i,j,k) + oy(i,j,k)*wy(i,j,k) + oz(i,j,k)*wz(i,j,k);
ez(i,j,k)= ez(i,j,k)+ (dnw - wnd);
end
end
end