Abstract: In this work, we present a numerical treatment of the model of two-phase flow in porous media including specific interfacial area. For numerical discretization we use the cell-centered finite difference (CCFD) method based on the shifting-matrices method which could reduce the time-consuming operations. A new iterative implicit algorithm has been developed to solve the problem under consideration. All advection and advection-like terms that appear in saturation equation and interfacial area equation are treated using upwind schemes together with the CCFD and shifting-matrices techniques. Selected simulation results such as $p_c-S_w-a_{wn}$ surface have been introduced. The simulation results have a good agreement with those in the literature using either pore network modeling or Darcy scale modeling.

Abstract: The research extends and improves the parametric study of "Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid" of Jenny et al. (2004) with special focus on the onset of chaos and on chaotic states. The results show that the effect of density ratio responsible for two qualitatively different oblique oscillating states has a significant impact both on the onset of chaos and on the behavior of fully chaotic states. The observed difference between dense and light spheres is associated to the strength of coupling between fluid and solid degrees of freedom. While the low frequency mode of oblique oscillating state presents specific features due to a strong solid - fluid coupling, the dynamics of the high frequency mode is shown to be driven by the same vortex shedding as the wake of a fixed sphere. The different fluid-solid coupling also determines two different ways how chaos sets in. Two outstanding ordered regimes are evidenced and investigated in the chaotic domain. One of them, characteristic for its helical trajectories, might provide a link to the experimentally evidenced, but so far numerically unexplained, vibrating regime of ascension of light spheres. For fully chaotic states, it is shown that statistical averaging converges in a satisfactory manner. Several statistical characteristics are suggested and evaluated.

Abstract: Recently, we have developed several techniques in order to accelerate Monte Carlo (MC) molecular simulations. For that purpose, two strategies were followed. In the first, new algorithms were proposed as a set of early rejection schemes performing faster than the conventional algorithm while preserving the accuracy of the method. On the other hand, a reweighting and reconstruction scheme was introduced that is capable of retrieving primary quantities and second derivative properties at several thermodynamic conditions from a single MC Markov chain. The latter scheme, was first developed to extrapolate quantities in NVT ensemble for structureless Lennard-Jones particles. However, it is evident that for most real life applications the NpT ensemble is more convenient, as pressure and temperature are usually known. Therefore, in this paper we present an extension to the reweighting and reconstruction method to solve NpT problems utilizing the same Markov chains generated by the NVT ensemble simulations. Eventually, the new approach allows elegant switching between the two ensembles for several quantities at a wide range of neighboring thermodynamic conditions.

Abstract: The paper presents a mathematical model of a turbulent river flow based on unsteady shallow water equations and depth averaged turbulence model. The numerical model is based on upwind finite volume method on structured staggered grid. In order to get a stable numerical solution simple-based algorithm was used. Among well-developed models of the river flow proposed approach stands out with its computational efficiency and high quality in describing processes in a river stream. For the main cases of pollution transport in river flows it is essential to know whether the model is appropriate to predict turbulent characteristics of the flow in the open channel. Two computational cases have been carried out to investigating and to applying established model. The first case shows the impact of confluents into generation of turbulence in the river flow and shows that recirculation flows effects on the process of pollutant dispersion in water basins. Driven cavity test case have been carried out to investigate the accuracy of the established method and its applicability to the streams with a complex structure.