LXX
(LXX)
1
Hello, everyone.

I want to solev MHD equations in freefem++, but I really can not deal with the boundary condition of magnetic B, especially the condition

```
B·n = 0
```

or

```
B·n = Be·n
```

Be is the analytic solution and n is the normal for boundary.

The MHD equations as follows, where time J = [0,T],

Another question: In three dimensions, I define the mesh

```
mesh3 Th = cube(N,N,N);
```

But when N > 10, the output: out of memory. Are there somes methods to this?

fb77
(François Bouchut)
2
You can do as

The penalty formulation (3) will work if the boundary is made of flat pieces. Otherwise you have to lump it, see

Boundary condition - #6 by fb77

LXX
(LXX)
3
For `B·n = Be·n`

in boundary of three dimensions \Omega, is it okay for me to enter like this?

```
+ int2d(Th, 1, 2, 3, 4, 5, 6)(1e10*( Bx*N.x + By*N.y + Bz*N.z )*( wx*N.x + wy*N.y + wz*N.z ) )
- int2d(Th, 1, 2, 3, 4, 5, 6) (1.e10*( Bxe*N.x + Bye*N.y + Bze*N.z )*( wx*N.x + wy*N.y + wz*N.z ) )
```

Is there need any other statements for magnetics `B`

, like

```
+ on(1, 2, 3, 4, 5, 6)(.......)
```

fb77
(François Bouchut)
4
Yes it looks good (if your domain has flat boundaries as I said, like a cube for example). There is no need of anything else.

fb77
(François Bouchut)
5
For completeness I explain why the variational formulation corresponds to your required boundary condition.