Open Boundary Condition for Diffusion Equation
I'm trying to solve a simple one-D diffusion equaiton
S_t - D S_xx =0
in a infinite domain x= -inf to x= +inf. I'm using a BTCS scheme which is always stable. But question is how should I deal with open boundary condition since my compute domain is x=-L to x=L ? Some suggst use S_xx=0 at the OBC. Yet, from a point source analytical solution, we have
S(x,t)= A/sqrt(2Dt) * exp(-x^2/(4Dt))
so at the boundary x=-L, and x=L, analytical solution is > 0 when t>0 and also S_t \= 0. If I set S_xx =0, I will get S_t =0 which is not true. Your suggestion?
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