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We present a novel computational framework for diffusive-reactive systemsthat satisfies the non-negative constraint and maximum principles on generalcomputational grids. The governing equations for the concentration of reactantsand product are written in terms of tensorial diffusion-reaction equations. %We restrict our studies to fast irreversible bimolecular reactions. If oneassumes that the reaction is diffusion-limited and all chemical species havethe same diffusion coefficient, one can employ a linear transformation torewrite the governing equations in terms of invariants, which are unaffected bythe reaction. This results in two uncoupled tensorial diffusion equations interms of these invariants, which are solved using a novel non-negative solverfor tensorial diffusion-type equations. The concentrations of the reactants andthe product are then calculated from invariants using algebraic manipulations.The novel aspect of the proposed computational framework is that it will alwaysproduce physically meaningful non-negative values for the concentrations of allchemical species. Several representative numerical examples are presented toillustrate the robustness, convergence, and the numerical performance of theproposed computational framework. We will also compare the proposed frameworkwith other popular formulations. In particular, we will show that the Galerkinformulation (which is the standard single-field formulation) does not producereliable solutions, and the reason can be attributed to the fact that thesingle-field formulation does not guarantee non-negative solutions. We willalso show that the clipping procedure (which produces non-negative solutionsbut is considered as a variational crime) does not give accurate results whencompared with the proposed computational framework.

A numerical framework for diffusion-controlled bimolecular-reactive systems to enforce maximum principles and non-negative constraint