Related papers: Benchmarks for infinite medium, time dependent tra…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
The set of benchmark solutions used in the thermal radiative transfer community suffer some coverage gaps, in particular nonlinear, non-equilibrium problems. Also, there are no non-equilibrium, optically thick benchmarks. These shortcomings…
In non-classical linear transport the chord length distribution between collisions is non-exponential and attenuation does not respect Beer's law. Generalized radiative transfer (GRT) extends the classical theory to account for such…
For the purpose of finding benchmark quality solutions to time dependent Sn transport problems, we develop a numerical method in a Discontinuous Galerkin (DG) framework that utilizes time dependent cell edges, which we call a moving mesh,…
This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin,…
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network and imposes the boundary condition via a Lagrange multiplier,…
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…
Two benchmark problems for linear radiation transport and derived from the literature are presented in detail and several quantities of interest are defined. High-resolution simulations are computed using standard, robust numerical methods…
We have proposed an analytical approach for exact solution of multi-channel scattering problems, in presence of Dirac Delta function couplings. Our solution is quite general and is valid for any set of potentials, if the Green's functions…
The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of P\'eclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these…
Networks of interconnected resistors, springs and beams, or pores are standard models of studying scalar and vector transport processes in heterogeneous materials and media, such as fluid flow in porous media, and conduction, deformations,…
Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy…
The Non-Equilibrium Green's Function (NEGF) method combined with ab initio calculations has been widely used to study charge transport in molecular junctions. However, the significant computational demands of high-resolution calculations…
This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…
This paper is concerned with numerical solution of transport problems in heterogeneous porous media. A semi-discrete continuous-in-time formulation of the linear advection-diffusion equation is obtained by using a mixed hybrid finite…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
The statistics of a passive scalar randomly emitted from a point source is investigated analytically. Our attention has been focused on the two-point equal-time scalar correlation function. The latter is indeed easily related to the…
As manifested in the similarity relation of diffuse light transport, it is difficult to assess single scattering characteristics from multiply scattered light. We take advantage of the limited validity of the diffusion approximation of…