Stochastic flow simulation and particle transport in a 2D layer of random porous medium

A stochastic numerical method is developed for simulation of flows and particle transport in a 2D layer of porous medium. The hydraulic conductivity is assumed to be a random field of a given statistical structure, the flow is modeled in the layer with prescribed boundary conditions. Numerical experiments are carried out by solving the Darcy equation for each sample of the hydraulic conductivity by a direct solver for sparse matrices, and tracking Lagrangian trajectories in the simulated flow. We present and analyze different Eulerian and Lagrangian statistical characteristics of the flow such as transverse and longitudinal velocity correlation functions, longitudinal dispersion coefficient, and the mean displacement of Lagrangian trajectories. We discuss the effect of long-range correlations of the longitudinal velocities which we have found in our numerical simulations. The related anomalous diffusion is also analyzed.researc

Analysis of relative dispersion of two particles by Lagrangian stochastic models and DNS methods

Comparisons of the Q1D against the known Lagrangian stochastic well-mixed quadratic form models and the moments approximation models are presented. In the case of modestly large Reynolds numbers turbulence (Re λ ⋍ 240) the comparison of the Q1D model with the DNS data is made. Being in a qualitatively agreemnet with the DNS data, the Q1D model predicts higher rate of separation. Realizability of Q1D model extracted from the transport equation with a quadratic form of the conditional acceleration is shown

Lidar investigations of M-zone

The creation of pulse dye lasers tuned to resonant line of meteor produced admixtures of atmospheric constituents has made it possible to begin lidar investigations of the vertical distribution of mesospheric sodium concentration and its dynamics in the upper atmosphere. The observed morning increase of sodium concentration in the vertical column is probably caused by diurnal variations of sporadic meteors. The study of the dynamics of the sodium column concentration in the period of meteor streams activity confirms the suggestion of cosmic origin of these atoms. The short lived increase of sodium concentration brought about by a meteor stream, however, exceeds by one order the level of the sporadic background

Exponential bounds for the probability deviations of sums of random fields

Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field

Coagulation of Aerosol Particles in Turbulent Flows

. -- Coagulation of particles in turbulent flows is studied. The size distribution of particles is governed by Smoluchowski equation with random collision coefficient. The random coagulation coefficient is derived by a generalization of the approach suggested by Saffman and Turner [12]. The coagulation process is analysed in three main cases: (1) T c , the characteristic coagulation time is much less than Tw , the characteristic Lagrangian time of the turbulent flow, (2) conversely, Tw !! T c , and (3), these times are of the same order: Tw ¸ T c . A special stochastic time is introduced which drastically simplifies the analysis of the influence of the intermittency. A detailed numerical study is given for two cases with known explicit solutions of Smoluchowski equation. The numerical analysis in the turbulent collision regime is based on the stochastic algorithm presented in the book [9] and developed in [11], [10], and [4]. 1 Introduction The coagulation processes of aerosol particl..

Lognormal random field approximations to LIBOR market models

We study several approximations for the LIBOR market models presented in [1, 2, 5]. Special attention is payed to log-normal approximations and their simulation by using direct simulation methods for log-normal random fields. In contrast to the conventional numerical solution of SDE's this approach simulates the solution directly at the desired point and is therefore much more efficient. We carry out a path-wise comparison of the approximations and give applications to the valuation of the swaption and the trigger swap. 1 Introduction By far the most important class of traded interest rate derivatives is constituted by derivatives which are specified in terms of LIBOR rates. The LIBOR 1 rate L is the annualized effective interest rate over a forward period [T 1 ; T 2 ] and can be expressed in terms of two zero-coupon bonds B 1 and B 2 with face value $1; maturing at T 1 and T 2 ; respectively, L(t; T 1 ; T 2 ) := B1 (t) B2 (t) \Gamma 1 T 2 \Gamma T 1 ; (1) where as usual T 2 is..