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The self-adjoint angular flux and streamline-upwind Petrov-Galerkin transport equations are discretized using reproducing kernels with the collocation method to produce a discretization that is compatible with conservative reproducing kernel smoothed particle hydrodynamics. A novel second derivative is derived for the diffusion-like term in the self-adjoint angular flux equation. The resulting equations involve only evaluations of kernels and physical data at the nodal centers.
The time-dependent radiation transport equation is discretized using the meshless-local Petrov-Galerkin method with reproducing kernels. The integration is performed using a Voronoi tessellation, which creates a partition of unity that only depends o
A pore network modeling (PNM) framework for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst-Planck (NP) equations for each charged species in the electrolytic solution in addition to
The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for incompres
Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that describes
The nonequilibrium Greens function (NEGF) method is often used to predict transport in atomistically resolved nanodevices and yields an immense numerical load when inelastic scattering on phonons is included. To ease this load, this work extends the