Related papers: Splitting Approach for Solving Multi-Component Tra…
Directly computing mass transport coefficients in stochastic models requires integrating over time the equilibrium correlations between atomic displacements. Here, we show how to accelerate the computations via \green{correlation splitting…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
Detailed calculations of the transport coefficients of a recently introduced particle-based model for fluid dynamics with a non-ideal equation of state are presented. Excluded volume interactions are modeled by means of biased stochastic…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
Dimensionally split advection schemes are attractive for atmospheric modelling due to their efficiency and accuracy in each spatial dimension. Accurate long time-steps can be achieved without significant cost using the flux-form…
Diffusion models have demonstrated exceptional performances in various fields of generative modeling, but suffer from slow sampling speed due to their iterative nature. While this issue is being addressed in continuous domains, discrete…
This paper provides an initial description of the Method of Simultaneous Solutions, a Monte Carlo approach that simultaneously solves multiple Boltzmann-transport-like phenomena. Here, it is used to simultaneously solve the neutron…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the…
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying…
Using accurate multi-component diffusion treatment in numerical combustion studies remains formidable due to the computational cost associated with solving for diffusion velocities. To obtain the diffusion velocities, for low density gases,…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations…
In this article, we present an extension of the splitting algorithm proposed in [22] to networks of conservation laws with piecewise linear discontinuous flux functions in the unknown. We start with the discussion of a suitable Riemann…
Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of…
We present a general phase-space kinetic model for charged particle transport through combined localised and delocalised states, capable of describing scattering collisions, trapping, detrapping and losses. The model is described by a…
In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the…
The Boltzmann equation for $d$-dimensional inelastic Maxwell models is considered to analyze transport properties for monodisperse gas-solid suspensions. The influence of the interstitial gas phase on the dynamics of solid particles is…