Search results for "Continuity equation"
showing 10 items of 14 documents
Dimensionless Stage-Discharge Relationship for a Non-Linear Water Reservoir: Theory and Experiments
2020
In the field of hydrology, stage&ndash
Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule
2016
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such…
Two-Dimensional Modeling of a Flat-Plate Photocatalytic Reactor for Oxidation of Indoor Air Pollutants
2007
In this paper we present a two-dimensional (2-D) analysis of a narrow-slit, flat-plate, single-pass, flow-through photocatalytic reactor for air purification. The continuity equation for convection and diffusion in two dimensions, under un-steady-state conditions, was coupled with radiation field modeling and photocatalytic reaction kinetics to model the transient and steady-state behavior of the reactor. The model was applied to the photocatalytic oxidation of trichloroethylene (TCE) in humidified air streams under different experimental conditions. The kinetic parameters determined by a three-dimensional (3-D) computational fluid dynamics model of the reactor were used in the 2-D model si…
Rigorous investigation of RF breakdown effects in high power microstrip passive circuits
2009
This work presents a new rigorous investigation of corona effects in microstrip components. To carry out the investigation, a new software tool has been developed. The new tool first calculates the electromagnetic fields in complex microstrip structures using a Volume Integral Equation (VIE) formulation. Novel numerical techniques have been incorporated in the VIE to increase the accuracy during the computation of the electromagnetic fields. This includes novel techniques introduced to treat the singularities of the Green's functions. Once the electromagnetic fields are computed accurately, corona effects in the relevant structures are investigated. For this, a numerical solution of the fre…
Effect of Heat Exchange Transient Conditions with Moving Water-Air Interface on Space Charge Accumulation in Undersea HVdc Cables
2021
The accumulation of space charge inside the dielectric layer of an HVdc cable is one of the most important issue to be considered in the design stage and during the operating conditions. The separation of space charge is due to several factors including the dependence on temperature of the electrical conductivity of the insulation and the establishment of a thermal gradient under load conditions. This article is focused on the investigation of the effect of an axial heat transmission on the space charge and electric field distributions in an HVdc cable. In order to assess the impact of this phenomenon, a case study involving a cable immersed partly in water and partly in air has been simula…
The Application of CFD Methods for Modeling of a Three-Phase Fixed-Bed Reactor
2018
The mathematical model of the three-phase fixed-bed reactor (TBR) consisting of the continuity equation, the momentum balances of each phase and mass balances of reaction mixture components were presented and discussed. These balances are the result of averaging by means of Euler’s procedure and form the basis of the Computational Fluid Dynamics (CFD). Although the CFD model is based on fundamental principles some empirical relations (closure lows) must be implemented into the momentum balance in order to ensure a proper description of the dynamics of very complex three-phase system. Therefore, the sensitivity of a multiphase CFD model with respect to relations defining drag forces between …
A non-hydrostatic pressure distribution solver for the nonlinear shallow water equations over irregular topography
2016
Abstract We extend a recently proposed 2D depth-integrated Finite Volume solver for the nonlinear shallow water equations with non-hydrostatic pressure distribution. The proposed model is aimed at simulating both nonlinear and dispersive shallow water processes. We split the total pressure into its hydrostatic and dynamic components and solve a hydrostatic problem and a non-hydrostatic problem sequentially, in the framework of a fractional time step procedure. The dispersive properties are achieved by incorporating the non-hydrostatic pressure component in the governing equations. The governing equations are the depth-integrated continuity equation and the depth-integrated momentum equation…
A Positive Definite Advection Scheme for Use in Long Range Transport Models: Extension to Monotonicity
1992
Numerical modeling of atmospheric transport processes requires the solution of the continuity equation for prognostic variables such as momentum, heat, water vapor, liquid water or chemical species of the atmosphere. Although in the literature many advection schemes are known to solve this problem (Lax and Wendroff 1964, Crowley 1968, Tremback et al. 1987, Bott 1989a,b), these algorithms show different disadvantages, which sometimes yield undesirably poor numerical results. For instance, the upstream method is known to produce large numerical diffusion. The higher order versions of the advection schemes of Tremback et al. (1987) are much less diffusive. Unfortunately, the schemes are not po…
Pressure-flow dynamics with semi-stable limit cycles in hydraulic cylinder circuits
2021
In hydraulic circuits of the standard fluid-power actuators and mechanisms, like the linear-stroke cylinders, some hydrodynamic effects are often neglected. It happens mainly due to their complexity and secondariness in comparison with the principal transient and steady-state behavior of the hydromechanical process variables, such as the differential pressure and relative displacement and its rate, in other words the piston stroke and velocity. However, a constrained motion of the cylinder piston can give rise to the back coupled excitation of the pressure-flow dynamics, especially upon mechanical impact at the cylinder limits. Following to that, semi-stable limit cycles can arise while the…
Continuity equation and local gauge invariance for the N3LO nuclear energy density functionals
2011
Background: The next-to-next-to-next-to-leading order (N3LO) nuclear energy density functional extends the standard Skyrme functional with new terms depending on higher-order derivatives of densities, introduced to gain better precision in the nuclear many-body calculations. A thorough study of the transformation properties of the functional with respect to different symmetries is required, as a step preliminary to the adjustment of the coupling constants. Purpose: Determine to which extent the presence of higher-order derivatives in the functional can be compatible with the continuity equation. In particular, to study the relations between the validity of the continuity equation and invari…