Evolution equations in physical chemistry

textWe analyze a number of systems of evolution equations that arise in the study of physical chemistry. First we discuss the well-posedness of a system of mixing compressible barotropic multicomponent flows. We discuss the regularity of these variational solutions, their existence and uniqueness, and we analyze the emergence of a novel type of entropy that is derived for the system of equations. Next we present a numerical scheme, in the form of a discontinuous Galerkin (DG) finite element method, to model this compressible barotropic multifluid. We find that the DG method provides stable and accurate solutions to our system, and that further, these solutions are energy consistent; which is to say that they satisfy the classical entropy of the system in addition to an additional integral inequality. We discuss the initial-boundary problem and the existence of weak entropy at the boundaries. Next we extend these results to include more complicated transport properties (i.e. mass diffusion), where exotic acoustic and chemical inlets are explicitly shown. We continue by developing a mixed method discontinuous Galerkin finite element method to model quantum hydrodynamic fluids, which emerge in the study of chemical and molecular dynamics. These solutions are solved in the conservation form, or Eulerian frame, and show a notable scale invariance which makes them particularly attractive for high dimensional calculations. Finally we implement a wide class of chemical reactors using an adapted discontinuous Galerkin finite element scheme, where reaction terms are analytically integrated locally in time. We show that these solutions, both in stationary and in flow reactors, show remarkable stability, accuracy and consistency.Chemistry and Biochemistr

Dynamic p-enrichment schemes for multicomponent reactive flows

We present a family of p-enrichment schemes. These schemes may be separated into two basic classes: the first, called \emph{fixed tolerance schemes}, rely on setting global scalar tolerances on the local regularity of the solution, and the second, called \emph{dioristic schemes}, rely on time-evolving bounds on the local variation in the solution. Each class of $p$-enrichment scheme is further divided into two basic types. The first type (the Type I schemes) enrich along lines of maximal variation, striving to enhance stable solutions in "areas of highest interest." The second type (the Type II schemes) enrich along lines of maximal regularity in order to maximize the stability of the enrichment process. Each of these schemes are tested over a pair of model problems arising in coastal hydrology. The first is a contaminant transport model, which addresses a declinature problem for a contaminant plume with respect to a bay inlet setting. The second is a multicomponent chemically reactive flow model of estuary eutrophication arising in the Gulf of Mexico.Comment: 29 pages, 7 figures, 3 table

Reduced models for ETG transport in the pedestal

This paper reports on the development of reduced models for electron temperature gradient (ETG) driven transport in the pedestal. Model development is enabled by a set of 61 nonlinear gyrokinetic simulations with input parameters taken from the pedestals in a broad range of experimental scenarios. The simulation data has been consolidated in a new database for gyrokinetic simulation data, the Multiscale Gyrokinetic Database (MGKDB), facilitating the analysis. The modeling approach may be considered a generalization of the standard quasilinear mixing length procedure. The parameter η, the ratio of the density to temperature gradient scale length, emerges as the key parameter for formulating an effective saturation rule. With a single order-unity fitting coefficient, the model achieves an RMS error of 15%. A similar model for ETG particle flux is also described. We also present simple algebraic expressions for the transport informed by an algorithm for symbolic regression.</p

Discontinuous Galerkin method for multifluid Euler equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106454/1/AIAA2013-2595.pd