Cell size error in stochastic particle methods for coagulation equations with advection

The paper studies the approximation error in stochastic particle methods for spatially inhomogeneous population balance equations. The model includes advection, coagulation and inception. Sufficient conditions for second order approximation with respect to the spatial discretization parameter (cell size) are provided. Examples are given, where only first order approximation is observed

Cell size error in stochastic particle methods for coagulation equations with advection

The paper studies the approximation error in stochastic particle methods for spatially inhomogeneous population balance equations. The model includes advection, coagulation and inception. Sufficient conditions for second order approximation with respect to the spatial discretization parameter (cell size) are provided. Examples are given, where only first order approximation is observed

A stochastic weighted particle method for coagulation-advection problems

A spatially resolved stochastic weighted particle method for inception--coagulation--advection problems is presented. Convergence to a deterministic limit is briefly studied. Numerical experiments are carried out for two problems with very different coagulation kernels. These tests show the method to be robust and confirm the convergence properties. The robustness of the weighted particle method is shown to contrast with two Direct Simulation Algorithms which develop instabilities

Properties of the solutions of delocalised coagulation and inception problems with outflow boundaries

Well posedness is established for a family of equations modelling particle populations undergoing delocalised coagulation, advection, inflow and outflow in a externally specified velocity field. Very general particle types are allowed while the spatial domain is a bounded region of $d$-dimensional space for which every point lies on exactly one streamline associated with the velocity field. The problem is formulated as a semi-linear ODE in the Banach space of bounded measures on particle position and type space. A local Lipschitz property is established in total variation norm for the propagators (generalised semi-groups) associated with the problem and used to construct a Picard iteration that establishes local existence and global uniqueness for any initial condition. The unique weak solution is shown further to be a differentiable or at least bounded variation strong solution under smoothness assumptions on the parameters of the coagulation interaction. In the case of one spatial dimension strong differentiability is established even for coagulation parameters with a particular bounded variation structure in space. This one dimensional extension establishes the convergence of the simulation processes studied in [Patterson, Stoch. Anal. Appl. 31, 2013] to a unique and differentiable limit

Explicit stochastic schemes for transport in particle-resolved simulations

Stochastic particle-resolved methods are a recent development in atmospheric aerosol modeling. These methods resolve individual aerosol particles to track the information of their composition during a numerical simulation. This enables the detailed analysis of aerosol and gas-phase chemistry, and allows for a more accurate estimate of the aerosol impact on human health and Earth's climate. Transport of all particles in a finite-volume framework can be represented as a stochastic model with each particle having a probability to commute between neighboring grid-cells. This work develops and illustrates the stochastic particle-resolved transport method, which can be used for aerosol transport in atmosphere. The development of the stochastic model was inspired by the passive scalar transport in a predefined velocity field. The model was developed by splitting the transport process into advection and diffusion, and combining them with superposition. Single time-step explicit advection schemes and a Range-kutta numerical scheme were compared to the deterministic advection equation solutions and analytical solutions. The analysis also includes the stochastic modeling of the diffusion process and its results compared to analytical solution. For all cases, a quantification of total error and a numerical convergence analysis is presented

Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates

We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles. We derive the equation for the macroscopic density of particles, perform a linear stability analysis on it, and show that there is a finite-wavelength instability leading to pattern formation. This is the responsible for the approximate periodicity with which the clusters of particles arrange in the microscopic model. In addition, we consider the population when immersed in a fluid medium and analyze the influence of advection on global properties of the model.Comment: Some typos and some problems with the figures correcte

Wind-Driven Gas Networks and Star Formation in Galaxies: Reaction-Advection Hydrodynamic Simulations

The effects of wind-driven star formation feedback on the spatio-temporal organization of stars and gas in galaxies is studied using two-dimensional intermediate-representational quasi-hydrodynamical simulations. The model retains only a reduced subset of the physics, including mass and momentum conservation, fully nonlinear fluid advection, inelastic macroscopic interactions, threshold star formation, and momentum forcing by winds from young star clusters on the surrounding gas. Expanding shells of swept-up gas evolve through the action of fluid advection to form a ``turbulent'' network of interacting shell fragments whose overall appearance is a web of filaments (in two dimensions). A new star cluster is formed whenever the column density through a filament exceeds a critical threshold based on the gravitational instability criterion for an expanding shell, which then generates a new expanding shell after some time delay. A filament- finding algorithm is developed to locate the potential sites of new star formation. The major result is the dominance of multiple interactions between advectively-distorted shells in controlling the gas and star morphology, gas velocity distribution and mass spectrum of high mass density peaks, and the global star formation history. The gas morphology observations of gas in the LMC and in local molecular clouds. The frequency distribution of present-to-past average global star formation rate, the distribution of gas velocities in filaments (found to be exponential), and the cloud mass spectra (estimated using a structure tree method), are discussed in detail.Comment: 40 pp, 15 eps figs, mnras style, accepted for publication in MNRAS, abstract abridged, revisions in response to referee's comment