A quasi-analytical approach to the advection–diffusion–reaction problem, using operator splitting

• A novel quasi-analytical technique to solve the ADR equation is proposed.
• Advection, diffusion & reaction are each solved analytically; combined numerically.
• Simple examples demonstrate the application and results of the technique.
• The technique eliminates truncation error suffered by purely numerical methods.
• For special cases, the technique gives an exact solution.

Solutions of the combined advection–diffusion–reaction (ADR) transport equation are generally restricted to numerical methods. However, each subprocess, advection, diffusion and reaction can all be solved individually using analytical techniques for a variety of situations. We present a simple numerical technique that uses the split operator method, and the Semi-Lagrangian scheme, to combine these analytical solutions. The result is a coherent, quasi-analytical solution to the combined ADR transport equation.