Hello:
I want to know how to use a numerical boundary condition in deal.II. For
example, I want to solve a set of diffusion equations:
\partial c_1 / \partial t = d_1 \partial c_1^2 / \partial x^2
\partial c_2 / \partial t = d_2 \partial c_2^2 / \partial x^2
on the one dimensional domain [0, L].
At the right boundary, the Dirichlet boundary condition is applied: c_1(x =
L, t) = c_{10}, c_2(x = L, t) = c_{20}.
At the left boundary, the flux of c_1, c_2 is set by:
*\partial c_1 / \partial x (x = 0, t) = r_1(c_1, c_2)*
*\partial c_2 / \partial x (x = 0, t) = r_2(c_1, c_2)*
Here, r1 r2 are reactions rates solved by an ODE solver. Then how to use
such a boundary condition ? There is no analytic expression for r1 and r2.
I can only get them numerically. [image: 屏幕截图 2023-12-16 095822.jpg]
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