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.
