Use advection step and Dispersion step to solve advection diffusion equation
I have been trying to use the TVD scheme for the advection term in advection diffusion equation. I was wondering how can I solve the equation in two steps. In the first step I want to solve for the advection and in the next step I want to solve for the dispersion. I will use TVD scheme to solve for the advection and I will use the central difference scheme to solve for the dispersion term. Have any of you tried to solve this problem using two step method ? I have solved the advection equation only with the TVD scheme but when I add the dispersion term also and solve by using the central difference I somehow don't get the required result. Any help or starting point to solve this problem is highly appreciated.
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