Related papers: Modeling and analysis of pooled stepped chutes
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
In this paper, we consider a system of partial differential equations modeling the evolution of a landscape. A ground surface is eroded by the flow of water over it, either by sedimentation or dilution. The system is composed by three…
Analyzing field data from pumping tests, we show that as with many other natural phenomena, groundwater flow exhibits a complex dynamics described by 1/f power spectrum. This result is theoretically studied within an agent perspective.…
Stochastic computational models in the form of pure jump processes occur frequently in the description of chemical reactive processes, of ion channel dynamics, and of the spread of infections in populations. For spatially extended models,…
The Schroedinger equation with a potential periodically varying in time is used to model adiabatic quantum pumps. The systems considered may be either infinitely extended and gapped or finite and connected to gapless leads. Correspondingly,…
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross…
We consider split-step Milstein methods for the solution of stiff stochastic differential equations with an emphasis on systems driven by multi-channel noise. We show their strong order of convergence and investigate mean-square stability…
A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…
In many natural and industrial applications, turbulent flows encompass some form of dispersed particles. Although this type of multiphase turbulent flow is omnipresent, its numerical modeling has proven to be a remarkably challenging…
We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions…
Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume…
We study the step bunching process in three different 1D step flow models and obtain scaling relations for the step bunches formed in the long times limit. The first one was introduced by S.Stoyanov [Jap. J.Appl. Phys. 29, (1990) L659] as…
We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of boundary conditions is proposed which make these equations well-posed. Several different cases occur depending on the relative values of the reference…
Consider a balance law where the flux depends explicitly on the space variable. At jump discontinuities, modeling considerations may impose the defect in the conservation of some quantities, thus leading to non conservative products. Below,…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
Slug flows are a typical intermittent two-phase flow pattern that can occur in submarine pipelines connecting the wells to the production facility and that is known to cause undesired consequences. In this context, computational fluid…
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress to the fluid and the fluid carries and…
The Cellular Potts Model (CPM) succesfully simulates drainage and shear in foams. Here we use the CPM to investigate instabilities due to the flow of a single large bubble in a dry, monodisperse two-dimensional flowing foam. As in…
Numerical algorithm for direct simulation of the gas flow in the Holweck pump is developed. The results illustrating the important features of the flow in the pump are reported. An attention is paid to the problem of the pump design…