Add constraint to Coupled PDEs

[Wenjiang Huang]

Hi,

I have a four coupled PDEs, where u3 + u4 is equal to 1. How can I add this constraint in my pefunc? Someone suggest replacing u4 as (1-u3), but I actually wanna output both u3 and u4 and to see if their sum is 1 to check my result.

below is the part of my pefunc:

f1 = -d_Fev*(u(1)*dudx(3)-u(3)*dudx(1))+d_Crv*(u(1)*dudx(3)+u(4)*dudx(1));
f2 = d_Fei*(u(2)*dudx(3)+u(3)*dudx(2)) - d_Cri*(u(2)*dudx(3)u(4)*dudx(2));
s2 = d_Fei*2*dudx(2)*dudx(3)+d_Cri*2*dudx(2)*dudx(3);
f3 = d_Fei*(u(2)*dudx(3)+u(3)*dudx(2)) +d_Fev*(u(1)*dudx(3)u(3)*dudx(1));
s3 = d_Fei*2*dudx(2)*dudx(3);
f4 = d_Cri*(u(2)*dudx(4)+u(4)*dudx(2)) + d_Cr*(u(1)*dudx(4)u(4)*dudx(1));
s4 = d_Cri*2*dudx(2)*dudx(4);
f = [f1;f2;f3;f4];
y=Ko-4*pi*d_rec/Omega*((d_Fev+d_Crv)*u(1)+(d_Fei+d_Cri)*u(2))*u(1)*u(2);
s = [y;y+s2;s3;s4];

My Bc:
pl = [ul(1) - C_v_t0; ul(2)-C_i_t0; 0; 0];
ql = [0;0;1;1];
pr = [0;0;0;0];
qr = [1;1;1;1];

where at x=0; flux for u3 and u4 is zero, and u1 u2

Many thanks,
WJ

[Wenjiang Huang]

Post by Wenjiang Huang
Hi,
I have a four coupled PDEs, where u3 + u4 is equal to 1. How can I add this constraint in my pefunc? Someone suggest replacing u4 as (1-u3), but I actually wanna output both u3 and u4 and to see if their sum is 1 to check my result.
f1 = -d_Fev*(u(1)*dudx(3)-u(3)*dudx(1))+d_Crv*(u(1)*dudx(3)+u(4)*dudx(1));
f2 = d_Fei*(u(2)*dudx(3)+u(3)*dudx(2)) - d_Cri*(u(2)*dudx(3)u(4)*dudx(2));
s2 = d_Fei*2*dudx(2)*dudx(3)+d_Cri*2*dudx(2)*dudx(3);
f3 = d_Fei*(u(2)*dudx(3)+u(3)*dudx(2)) +d_Fev*(u(1)*dudx(3)u(3)*dudx(1));
s3 = d_Fei*2*dudx(2)*dudx(3);
f4 = d_Cri*(u(2)*dudx(4)+u(4)*dudx(2)) + d_Cr*(u(1)*dudx(4)u(4)*dudx(1));
s4 = d_Cri*2*dudx(2)*dudx(4);
f = [f1;f2;f3;f4];
y=Ko-4*pi*d_rec/Omega*((d_Fev+d_Crv)*u(1)+(d_Fei+d_Cri)*u(2))*u(1)*u(2);
s = [y;y+s2;s3;s4];
pl = [ul(1) - C_v_t0; ul(2)-C_i_t0; 0; 0];
ql = [0;0;1;1];
pr = [0;0;0;0];
qr = [1;1;1;1];
where at x=0; flux for u3 and u4 is zero, and u1 u2

u1, u2 is constant. at x=1, du3/dt = du4/dt= divegence flux = 0, and flux for u1 and u2 is zero

Post by Wenjiang Huang
Many thanks,
WJ