SCI Publications

In an earlier study of inexact Newton methods, we pointed out that certain counterintuitive behavior may occur when applying residual backtracking to the Navier-Stokes equations with heat and mass transport. Specifically, it was observed that a Newton-GMRES method globalized by backtracking (linesearch, damping) may be less robust when high accuracy is required of each linear solve in the Newton sequence than when less accuracy is required. In this brief discussion, we offer a possible explanation for this phenomenon, together with an illustrative numerical experiment involving the Navier-Stokes equations.

The emphasis in this paper is on presenting a new methodology, together with some illustrative applications, for the study of polycyclic aromatic hydrocarbon polymerization leading to soot, widely recognized as a very important and challenging combustion problem. The new code, named fully integrated Kinetic Monte Carlo/Molecular Dynamics (KMC/MD), places the two simulation procedures on an equal footing and involves alternating between KMC and MD steps during the simulation. The KMC/MD simulations are used in conjunction with high-level quantum chemical calculations. With traditional kinetic rates and dealing with the growth of particles, it is often necessary to perform a lurnping procedure in which much atomic-scale information is lost. Our KMC/MD approach is designed to preserve atomic-scale structure: a single particle evolves in time with real three-dimensional structure (bonds, bond angles, dihedralangles). In this paper, the methodology is illustrated by a sample simulation of high molecular mass compound growth in an environment (T, H, H₂, naphthalene, and acenaphthylene concentrations) of a low-pressure laminar premixed benzene/oxygen/argon flame with an equivalence ratio of 1.8. The use of this approach enables the investigation of the physical (e.g., porosity, density, sphericity) as well as chemical (e.g. H/C, aromatic moieties, number of cross-links) properties.

Pathways for the growth of high-molecular-mass compounds are presented, showing how reactions between aromatic moieties can explain recent experimental findings. A fundamental molecular analysis of polycyclic aromatic hydrocarbon growth processes in combustion systems involving five-membered ring compounds is presented using quantum mechanical density functional methods. Higher aromatics are produced through a two-step radical-molecule addition reaction and the iteration of this mechanism followed by rearrangement of the carbon framework ultimately leads to high-molecular-mass compounds. The distinguishing features of the proposed model lie in the chemical specificity of the routes considered. Naphthalene and acenaphthylene are used as examples of the aromatic and cyclopentafused aromatic classes of compounds postulated to be of importance in molecular weight growth. These reaction pathways are analyzed with a view toward explaining recent experimental findings on H/C ratio, NMR, and LMMS of soot precursors.

Jet A and JP-8 are kerosene fuels used in aviation and consist of complex mixtures of higher order hydrocarbons, including alkanes, cycloalkanes, and aromatic molecules. The objectives of the current work are to develop a surrogate mixture to represent JP-8 fuels and to discuss a general detailed chemical kinetic model for jet fuels, which is suitable for future reduction. Asurrogate blend of six pure hydrocarbons is found to adequately simulate the distillation and compositional characteristics of a practical JP-8. A hierarchically constructed kinetic model already available for the oxidation of alkanes and simple aromatic molecules (benzene, toluene, ethylbenzene, xylene, etc.) is extended to include methylcyclohexane and tetralin as new reference fuel components. The kinetic model is validated through comparisons with experimental data for the pure components and it is also used to verify and predict the structures of laminar premixed flames of different pure components as well as conventional kerosene fuels.

We present a new method for solving stochastic differential equations based on Galerkin projections and extensions of Wiener's polynomial chaos. Specifically, we represent the stochastic processes with an optimum trial basis from the Askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error. Several continuous and discrete processes are treated, and numerical examples show substantial speed-up compared to Monte Carlo simulations for low dimensional stochastic inputs.

Keywords: polynomial chaos, Askey scheme, orthogonal polynomials, stochastic differential equations, spectral methods, Galerkin projection

We present a generalized polynomial chaos algorithm to model the input uncertainty and its propagation in flow-structure interactions. The stochastic input is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as the trial basis in the random space. A standard Galerkin projection is applied in the random dimension to obtain the equations in the weak form. The resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode. This approach is a generalization of the original polynomial chaos expansion, which was first introduced by N. Wiener (1938) and employs the Hermite polynomials (a subset of the Askey scheme) as the basis in random space. The algorithm is first applied to second-order oscillators to demonstrate convergence, and subsequently is coupled to incompressible Navier-Stokes equations. Error bars are obtained, similar to laboratory experiments, for the pressure distribution on the surface of a cylinder subject to vortex-induced vibrations.

We present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs. In particular, we focus on the solution of the Poisson equation with random diffusivity, forcing and boundary conditions. The stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the Askey scheme, as a generalization of the original polynomial chaos idea of Wiener [Amer. J. Math. 60 (1938) 897]. A Galerkin projection in random space is applied to derive the equations in the weak form. The resulting set of deterministic equations for each random mode is solved iteratively by a block Gauss–Seidel iteration technique. Both discrete and continuous random distributions are considered, and convergence is verified in model problems and against Monte Carlo simulations.

Keywords: Uncertainty, Random diffusion, Polynomial chaos