Open Boundary Condition for Diffusion Equation

wen long

Hi all,

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?

Thanks,

Wen