Oscillations around limit

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In my 1D model three variables are solved for. Temperature "T" and a solute concentration "c" are advected through a porous medium. The porous medium reacts with water and produces heat, using conversion variable "X". The reaction front moves as a travelling wave through the domain.

When reacting, the porous medium is converted from X=0 (initial value) to X=1 (fully converted). This means that between the inlet and the wave front, the conversion is 1 and between the wave front and the outlet the conversion is 0. The reaction rate is a function of T, c and X itself. To prevent numerical issues around X=0 and X=1 Heaviside functions are included.

The problem unfortunately is, that throughout the entire domain the values for T and c oscillate heavily, but especially where X=1 (see figure). The mesh is very fine and also the time step is restricted. I have played around with the solver settings but to no avail. Any other possible solutions for this?



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