Nathaniel Trask

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Modeling of the Internal Two-Phase Flow in a Gas-Centered Swirl Coaxial Fuel Injector

Predicting the liquid film dynamics inside the injector cup of gas-centered swirl coaxial fuel injectors requires a general two-phase approach that is appropriate for all liquid volume fractions, high Weber number, and complex geometries. The rapid exchange of momentum at the highly convoluted interface requires tight numerical coupling between the gas and liquid phases. An Eulerian two-phase model is implemented to represent the liquid and gas interactions in the injector as well as the atomization processes at the rough interface. The model, originally proposed by Vallet et al, assumes that in the limit of infinite Reynolds and Weber number, features of the atomization process acting at large length scales are separable from small scale mechanisms. A transport equation for the liquid volume fraction represents the dispersion of the liquid into the gas via a traditional turbulent diffusion hypothesis. A model for the growth of mean interfacial surface area is then used to characterize the growth of instability at the interface, allowing a characterization of Sauter mean diameter. The model shows promise as a computationally inexpensive tool for characterizing spray quality in regions where optical experimental data are difficult to obtain and two-phase direct numerical simulation methods are too demanding. Twodimensional results of the model are compared to photographs of the liquid film within the injector cup. The comparisons show good agreement between the predicted film profile and experimental measurements, although in some cases underpredicting the film length. The discrepancy between the experiment and model results suggest the need to extend the inter-phase coupling to a form more suitable for anisotropic, swirling flow.

A High-Order Staggered Meshless Method for Elliptic Problems

We present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points

Compact moving least squares: An optimization framework for generating high-order compact meshless discretizations

{\em x}_i

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the methods construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attains

Multidimensional modeling of condensing two-phase ejector flow

O(h^{m})

Intercomparison of 3D pore-scale flow and solute transport simulation methods

convergence in both

DIESEL SPRAY CFD SIMULATIONS BASED ON THE Σ-Υ EULERIAN ATOMIZATION MODEL

L^2

Compressible Modeling of the Internal Two-Phase Flow in a Gas-Centered Swirl Coaxial Fuel Injector

- and

A scalable consistent second-order SPH solver for unsteady low Reynolds number flows

H^1