Dirichlet boundary condition in heat equation

General Discussion
1

Hello fellows!

I’m trying to implement a simple bioheat problem, but I’m having trouble with the non homogeneous boundary condition.
The mesh is constructed using buildmesh and the problem is solved using varf.

Mesh

real n = 200; // mesh generation parameter
    real nom = 200;
    real nbody = 160;
    real ndes = 80;
   
    border pml01(t=0, 0.5){x=-0.5+2*t; y=-0.5;label=1;}
    border pml02(t=0, 0.5){x=0.5; y=-0.5+2*t;label=1;}
    border pml03(t=0, 0.5){x=0.5-2*t; y=0.5;label=1;}
    border pml04(t=0, 0.5){x=-0.5; y=0.5-2*t;label=1;}
    border om01(t=0, 0.25){x=-0.25+2*t;y=-0.25;label=2;}
    border om02(t=0, 0.25){x=0.25;y=-0.25+2*t;label=2;}
    border om03(t=0, 0.25){x=0.25-2*t;y=0.25;label=2;}
    border om04(t=0, 0.25){x=-0.25;y=0.25-2*t;label=2;}

    border b(t=0, 2*pi){x=0.1*cos(t); y=0.1*sin(t); label=3;}
    border d(t=0, 2*pi){x=0.03+0.02*cos(t); y=0.03+0.02*sin(t); label=4;}
    Th = buildmesh(pml01(n)+pml02(n)+pml03(n)+pml04(n)+om04(n)+om03(n)+om02(n)+om01(n)+b(nbody)+d(ndes));

Problem

varf bioheat(T,nu) = int2d(Th)(cK*dx(T)*dx(nu)+ dy(T)*dy(nu) + cw*T*nu) + on(1,T=25);
matrix Ah = bioheat(Oh,Oh, tgv=1e43);
varf bioheatrhs(T,nu) =  int2d(Th)(cw*thbb*nu);
fc[] = bioheatrhs(0,Oh);
T[] = Ah^-1 * fc[];

Note that I’m prescribing 25º in the boundary 1, but the result is 0º when I plot the solution using medit.

initial
initial751×787 64.8 KB

Someone knows how can I solve this issue?
Thanks in advance!

2

Note that I’m prescribing 25º in the boundary 1

No, you are not prescribing anything on the RHS.

1 Like
3

You could make a smaller mesh and dump matrix and rhs to see the problem.
Why can’t you use the same varf for both? What did you expect the tgv to do?

4

Change these lines to:

varf bioheatrhs(T,nu) =  int2d(Th)(cw*thbb*nu) + on(1,T=25);
fc[] = bioheatrhs(0,Oh, tgv=1e43);
1 Like
5

Thanks!
It worked perfectly fine.