Numerical simulation of chemical kinetics transport and flow processes

Abstract

In this thesis, numerical solution procedures are developed for simulating chemical phenomena. Mathematical models for phenomena involving flow, transport and reaction of chemical species are computationally challenging to simulate due to stiffness, high degrees of freedom and spatial dependence. Such challenges are resolved (in this thesis) by combining model decoupling techniques with compatible efficient numerical schemes. Chemical phenomena is decomposed into well-mixed chemical systems, poorly-mixed systems (or spatial dependent kinetics) and flow with reactive transport systems. Mathematical models for the systems are Ordinary Differential Equations (ODEs), parabolic Partial Differential Equations (PDEs) and hyperbolic PDEs, respectively. In the ODE model, stiffness is resolved by positivity-preserving implicit schemes while the large degrees of freedom is reduced by stoichiometric and continuous-time iteration methods. In the parabolic model, model decoupling techniques are employed to reduce the degrees of freedom while Implicit-Explicit numerical schemes are presented for resolving stiffness. Further, numerical schemes that have dispersion-dissipation-preserving properties have also been discussed. In the hyperbolic model, model decoupling techniques have been presented for reducing the degrees of freedom while shock-capturing, well-balanced numerical schemes have been presented for resolving nonlinear hyperbolic effects. The results from experiments show that the proposed numerical solution procedures can efficiently resolve the challenges in simulating chemical phenomena.