solving reaction-diffusion(-advection) equations?

[simulkade]

solving reaction-diffusion(-advection) equations?

[simulkade]

Hi @janelias1

Yes , you can solve this equation by first linearizing the source term u(1-u) = u-u^2.
The first u is discretized as M_s1 = linearSourceTerm(createCellVariablem, 1.0))
The second term is linearized to

u^2 = u_0^2 + 2u_0(u-u_0) = 2u_0*u - u_0^2

which can be linearized as

RHS_s1 = constantSourceTerm(u_val.^2) % u_val is a cell variable containing the current value of u
M_s2 = linearSourceTerm(2*u_val)

Send me your code if it still does not work.

[janelias1]

Thanks a lot! I tried indeed to use this linearisation (Taylor expansion) before but with no success: I don't obtain any travelling wave solution of the Fisher-KPP equation. So I thought that the problem is with the reaction term. Can you please have a look at the code? I have just sent the code to your outlook.com email. Many thanks in advance.