Question: moving boundary problem

Hi! I have some problems with solving convection-diffusion equation. The liquid phase move up with velocity W. And displace vapor phase. C - molar concentration of gas. z - coordinate. w - velocity. h - height of tank. t - time.

 

Its not clear to me how to set moving boundary condition on bottom boundary, so C(0,t)=cs must move up with w velocity.

May be maple have some procedures to make moving boundary or adaptive mesh??? thank you!

 

eq1 := diff(c(z, t), t)+diff(w*c(z, t), z) = d*(diff(c(z, t), z$2));
IBC := { c(z, 0) = 0, c(0, t) = cs, (D[1](c))(h, t) = 0}

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