We study a uniform flow in a parallel plate geometry to model contaminant transport through a saturated porous medium in a semi-infinite domain in order to simulate an experimental apparatus mainly constituted by a chamber filled with a glass beads bed. The general solution of the advection dispersion equation in a porous medium was obtained by utilizing the Jacobi ${\theta }_{3}$ Function. The analytical solution here presented has been provided when the inlet (Dirac) and the boundary conditions (Dirichelet, Neumann, and mixed types) are fixed. The proposed solution was used to study experimental data acquired by using a noninvasive technique.

We present and study a stabilized mixed finite element method for single-phase compressible flow through porous media. This method is based on a pressure projection stabilization method for multiple-dimensional incompressible flow problems by using the lowest equal-order pair for velocity and pressure (i.e., the ${\mathbf{P}}_1-P_1$ pair). An optimal error estimate in divergence norm for the velocity and suboptimal error estimates in the $L^2$-norm for both velocity and pressure are obtained. Numerical results are given in support of the developed theory.

The basic partial differential equation (PDE) models for supply chain networks with re-entrant nodes and their macroscopic are proposed. However, through numerical examples, the basic continuum models do not perform well for multiple re-entrant systems. Then, a new state equation considering the re-entrant degree of the products is introduced to improve the effectiveness of the basic continuum models. The applicability of the modified continuum models for re-entrant supply chains is illustrated through numerical examples. Finally, based on the modified continuum model, numerical examples of different re-entrant degrees are given, meanwhile, the changes in the WIP and outflux are analyzed in details for multiple re-entrant supply chain systems.

We introduce 2D numerical investigations of the problem of gravity and inlet/outlet location effects of water-oil two-phase cocurrent imbibition in a porous medium. Three different cases of side-, top-, and bottom-inlet location are considered. Two-dimensional computations are carried out using the finite element method. Intensive comparisons are done between considering and neglecting gravity effect on water saturation, pressures of water and oil as well as water velocity. Results are introduced either in curves or as 2D visualization graphs. The results indicate that the buoyancy effects due to gravity force take place depending on inlet location. So, the buoyancy force in the momentum equations of the co-current imbibition model cannot be neglected as done by several previous studies. Also, we note that the 2D zero gravity model has a uniform flow and may be represented as 1D flow unlike the 2D nonzero gravity model showing a nonuniform flow.

We aimed to derive a kernel function that accounts for the interaction among moving particles within the framework of particle method. To predict a computationally more accurate moving particle solution for the Navier-Stokes equations, kernel function is a key to success in the development of interaction model. Since the smoothed quantity of a scalar or a vector at a spatial location is mathematically identical to its collocated value provided that the kernel function is chosen to be the Dirac delta function, our guideline is to derive the kernel function that is closer to the delta function as much as possible. The proposed particle interaction model using the newly developed kernel function will be validated through the two investigated Navier-Stokes problems which have either the semianalytical or the benchmark solutions.

The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adjacent to an isothermal cone imbedded in a porous medium with Rosseland diffusion approximation incorporating the variation of permeability and thermal conductivity is numerically investigated. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Numerical results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed convection parameter $\chi$, the cone angle parameter $m$, the radiation-conduction parameter $R_d$, and the surface temperature parameter $H$.

We are motivated to model PE-CVD (plasma enhanced chemical vapor deposition) processes for metallic bipolar plates, and their optimization for depositing a heterogeneous layer on the metallic plate. Moreover a constraint to the deposition process is a very low pressure (nearly a vacuum) and a low temperature (about 400 K). The contribution of this paper is to derive a multiphysics system of multiple physics problems that includes some assumptions to simplify the complicate process and allows of deriving a computable mathematical model without neglecting the real-life processes. To model the gaseous transport in the apparatus we employ mobile gas phase streams, immobile and mobile phases in a chamber that is filled with porous medium (plasma layers). Numerical methods are discussed to solve such multi-scale and multi phase models and to obtain qualitative results for the delicate multiphysical processes in the chamber. We discuss a splitting analysis to couple such multiphysical problems. The verification of such a complicated model is done with real-life experiments for single species. Such numerical simulations help to economize on expensive physical experiments and obtain control mechanisms for the delicate deposition process.

Based on the stochastic concept for freeway capacity, the procedure of capacity estimation is developed. Due to the fact that it is impossible to observe the value of the capacity and to obtain the probability distribution of the capacity, the product-limit method is used in this paper to estimate the capacity. In order to implement estimation of capacity using this technology, the lifetime table based on statistical methods for lifetime data analysis is introduced and the corresponding procedure is developed. Simulated data based on freeway sections in Beijing, China, were analyzed and the results indicate that the methodology and procedure are applicable and validated.

The temporal discretization scheme is one important ingredient of efficient simulator for two-phase flow in the fractured porous media. The application of single-scale temporal scheme is restricted by the rapid changes of the pressure and saturation in the fractured system with capillarity. In this paper, we propose a multi-scale time splitting strategy to simulate multi-scale multi-physics processes of two-phase flow in fractured porous media. We use the multi-scale time schemes for both the pressure and saturation equations; that is, a large time-step size is employed for the matrix domain, along with a small time-step size being applied in the fractures. The total time interval is partitioned into four temporal levels: the first level is used for the pressure in the entire domain, the second level matching rapid changes of the pressure in the fractures, the third level treating the response gap between the pressure and the saturation, and the fourth level applied for the saturation in the fractures. This method can reduce the computational cost arisen from the implicit solution of the pressure equation. Numerical examples are provided to demonstrate the efficiency of the proposed method.

This paper begins with presenting a mathematical model for contaminant transport in the fractured vuggy porous media of a species of contaminant (PCP). Two phases are numerically simulated for a process of contaminant and clean water infiltrated in the fractured vuggy porous media by coupling mixed finite element (MFE) method and finite volume method (FVM), both of which are locally conservative, to approximate the model. A hybrid mixed finite element (HMFE) method is applied to approximate the velocity field for the model. The convection and diffusion terms are approached by FVM and the standard MFE, respectively. The pressure distribution and temporary evolution of the concentration profiles are obtained for two phases. The average effluent concentration on the outflow boundary is obtained at different time and shows some different features from the matrix porous media. The temporal multiscale phenomena of the effluent concentration on the outlet are observed. The results show how the different distribution of the vugs and the fractures impacts on the contaminant transport and the effluent concentration on the outlet. This paper sheds light on certain features of karstic groundwater are obtained.

Iterative splitting methods have a huge amount to compute matrix exponential. Here, the acceleration and recovering of higher-order schemes can be achieved. From a theoretical point of view, iterative splitting methods are at least alternating Picards fix-point iteration schemes. For practical applications, it is important to compute very fast matrix exponentials. In this paper, we concentrate on developing fast algorithms to solve the iterative splitting scheme. First, we reformulate the iterative splitting scheme into an integral notation of matrix exponential. In this notation, we consider fast approximation schemes to the integral formulations, also known as $\phi$-functions. Second, the error analysis is explained and applied to the integral formulations. The novelty is to compute cheaply the decoupled exp-matrices and apply only cheap matrix-vector multiplications for the higher-order terms. In general, we discuss an elegant way of embedding recently survey on methods for computing matrix exponential with respect to iterative splitting schemes. We present numerical benchmark examples, that compared standard splitting schemes with the higher-order iterative schemes. A real-life application in contaminant transport as a two phase model is discussed and the fast computations of the operator splitting method is explained.

The spatial distribution of parameters that characterize the subsurface is never known to any reasonable level of accuracy required to solve the governing PDEs of multiphase flow or species transport through porous media. This paper presents a numerically cheap, yet efficient, accurate and parallel framework to estimate reservoir parameters, for example, medium permeability, using sensor information from measurements of the solution variables such as phase pressures, phase concentrations, fluxes, and seismic and well log data. Numerical results are presented to demonstrate the method.

Thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension is numerically simulated using the single relaxation time lattice Boltzmann method (LBM). This problem is of considerable interest when dealing with cooling of microelectronic devices, in situations where natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid. Therefore, circulation is achieved by imposing a magnetic field, which is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection,” are analysed in terms of the flow modes and heat transfer characteristics of a magnetic fluid.

To investigate the influence of vascular normalization on solid tumor blood perfusion and drug delivery, we used the generated blood vessel network for simulations. Considering the hemodynamic parameters changing after antiangiogenic therapies, the results show that the interstitial fluid pressure (IFP) in tumor tissue domain decreases while the pressure gradient increases during the normalization window. The decreased IFP results in more efficient delivery of conventional drugs to the targeted cancer cells. The outcome of therapies will improve if the antiangiogenic therapies and conventional therapies are carefully scheduled.

Heat transfer enhancement technology has the aim of developing more efficient systems as demanded in many applications. An available passive method is represented by the employ of rough surfaces. Transversal turbulators enhance the heat transfer rate by reducing the thermal resistance near surfaces, because of the improved local turbulence; on the other hand, higher losses are expected. In this paper, a numerical investigation is carried out on turbulent water forced convection in a ribbed channel. Its external walls are heated by a constant heat flux. Several arrangements of ribs in terms of height, width, and shape are analyzed. The aim is to find the optimal configuration in terms of high heat transfer coefficients and low losses. The maximum average Nusselt numbers are evaluated for dimensionless pitches of 6, 8, and 10 according to the shape while the maximum friction factors are in the range of pitches from 8 to 10.

The numerical simulation of the water temperature in the Río de la Plata River and Montevideo's Bay was done using the numerical model of finite elements RMA-10 in its 2D vertical integrated mode. Parameters involved in the formulations of thermal exchange with the atmosphere were adjusted using measurements of water temperature in several locations of the water body. After calibrating the model, it was used to represent the operation of a power plant located in Montevideo's Bay. This central takes water from the bay in order to cool its generators and also discharges high-temperature water into the bay. The correct representation of temperatures at the water intake and discharge of the plant reflects that the model is able to represent the operation of the central. Several analysis were made to study the thermal plume, the effects of the water discharge on the water intake of the power plant, and the effect on environmental variables of the study area like currents.

We present a class of numerical methods for the reaction-diffusion-chemotaxis system which is significant for biological and chemistry pattern formation problems. To solve reaction-diffusion-chemotaxis systems, efficient and reliable numerical algorithms are essential for pattern generations. Along with the implementation of the method of lines, implicit or semi-implicit schemes are typical time stepping solvers to reduce the effect on time step constrains due to the stability condition. However, these two schemes are usually difficult to employ. In this paper, we propose an adaptive optimal time stepping strategy for the explicit $m$-stage Runge-Kutta method to solve reaction-diffusion-chemotaxis systems. Instead of relying on empirical approaches to control the time step size, variable time step sizes are given explicitly. Yet, theorems about stability and convergence of the algorithm are provided in analyzing robustness and efficiency. Numerical experiment results on a testing problem and a real application problem are shown.