In this work, an operator splitting method is proposed in order to obtain a stable numerical solution for transport equation with non-linear reaction term. We split the transport equation into a reaction part and an advection diffusion part. The former one which becomes a nonlinear ordinary differential equation can be approximated by the simple higher order integrator or solved exactly. The later one is approximated by the Streamline-Upwind Petrov-Galerkin (SUPG) method combined with the generalized Euler time integration (θ-method). Numerical results that illustrate the good performance of this method are reported.
Baysal, O., Tanoglu, G. (2012). An Operator Splitting Approximation Combined With The SUPG Method For Transport Equations With Nonlinear Reaction Term. CMES-Computer Modeling in Engineering & Sciences, 84(1), 27–40. https://doi.org/10.3970/cmes.2012.084.027
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