Fictitious Components Research Articles

Temperature-Displacement Fictitious Components in Thermoelasticity

A method of solving three-dimensional coupled quasi-static problems of linear thermoelasticity is presented. Any initial-boundary value problem contains a coupled initial state. The concept is based on extending a region occupied by the considered body over the whole space where the space value thermoelastic problem is formulated. Both the Helmholtz displacement potentials and temperature from the space value Helmholtz problem are convolutionally determined. All the outside component parts of the convolution products are here defined as fictitious ones. The solution of space value thermoelastic problem includes fictitious displacement-temperature components. Capacities of approximate fictitious components are calculated from the boundary condition contracted to the finite time interval. Approximate solution to the primary thermoelasticity problem is obtained by spatial contracting of the solution to the space value thermoelastic problem.

Stream CostsA First Screening of Reaction Pathways

The recent trend in the chemical industry is the rapid growth in the production of specialty chemicals, that is, specialty monomers, agricultural chemicals, pharmaceuticals, and so forth (high-value-added materials). The products produced often are very large molecules, and normally there are a very large number of reaction paths that can be used to produce them. Another feature of these multistep reaction problems is that the reaction chemistry usually is not completely known (a single reaction having a yield of less than unity is given or a single reaction that is not stoichiometrically balanced is reported for each reaction step). A first screening of these reaction paths can be accomplished by introducing fictitious reactions and/or fictitious components to account for the chemical uncertainties, and then using these approximations to calculate the raw materials costs and waste costs. Because the chemistry is not complete and the waste loads do not include separation system waste costs, all reaction paths within about 50% of the best should be retained for further consideration.

A model for predicting contaminant removal by adsorption within the International Space Station water processor: 1. Multicomponent equilibrium modeling.

A thermodynamic model is developed to predict adsorption equilibrium in the International Space Station water processor's multifiltration beds. The model predicts multicomponent adsorption equilibrium behavior using single-component isotherm parameters and fictitious components representing the background matrix. The fictitious components are determined by fitting total organic carbon and tracer isotherms with the ideal adsorbed solution theory. Multicomponent isotherms using a wastewater with high surfactant and organic compound concentrations are used to validate the equilibrium description on a coconut-shell-based granular activated carbon (GAC), coal-based GAC, and a polymeric adsorbent.

Fictitious component method of solving the schemes of the finite element method for elliptic boundary value problems with nonlocal boundary conditions in multiply connected domains

Fictitious component method of solving the schemes of the finite element method for elliptic boundary value problems with nonlocal boundary conditions in multiply connected domains

Removal of dissolved organic carbon using granular activated carbon

Granular activated carbon (GAC) is used to reduce disinfection by-products by removing dissolved organic carbon (DOC). The optimum empty bed contact time (EBCT) for a single adsorber was determined and the influence of parallel bed operation on GAC usage rate was examined using both pilot-plant data and mass transfer models. To describe the GAC performance using mass transfer models, the DOC was broken down into fictitious components, and individual fictive component equilibrium and mass transfer parameters were determined using bench scale laboratory studies. The complexities of model parameter determination are described and DOC removal in GAC pilot plants are compared to model predictions using parameters that were determined from bench scale scale tests.

DOMAIN DECOMPOSITION METHODS FOR SOLVING PDE's ON MULTI-PROCESSORS

In this paper, we discuss the parallel domain docomposition method (DDM) for solving PDE's on parallel computers. Three types of DDM: DDM with overlapping, DDM without overlapping and DDM with fictitious component are discussed in a uniform framework. The convergence of the asynchronous parallel algorithms based on DDM are discussed.

Fictitious components and subdomain alteranting methods

Fictitious components and subdomain alteranting methods

Strategies of domain decomposition for the design of parallel algorithms

This is a framework of the domain decomposition method (DDM) for solving PDEs on parallel computers. Three types of DDM: DDM with overlapping, DDM without overlapping and DDM with fictitious components are discussed in a uniform framework.

Fictitious components method and the modified difference counterpart of the Schwartz method

Fictitious components method and the modified difference counterpart of the Schwartz method

Two-stage fictitious components method for solving the Dirichlet boundary value problem

Article Two-stage fictitious components method for solving the Dirichlet boundary value problem was published on January 1, 1988 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 3, issue 4).

Two-stage fictitious components method for solving the wave Helmholtz equation

Article Two-stage fictitious components method for solving the wave Helmholtz equation was published on January 1, 1988 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 3, issue 5).

Application of the fictitious components method to the computation of the principal mode of a complex-shape RF cavity resonator

Application of the fictitious components method to the computation of the principal mode of a complex-shape RF cavity resonator

RF cavity computations by the domain decomposition and fictitious components methods

RF cavity computations by the domain decomposition and fictitious components methods

Fictitious component method for solving grid equations used to approximate higher-order elliptic equations with natural boundary conditions

Article Fictitious component method for solving grid equations used to approximate higher-order elliptic equations with natural boundary conditions was published on January 1, 1986 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 1, issue 1).

Equations of the mechanics of porous media saturated with liquid and gas

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.

Application of Stiffly Stable Algorithms in the Digital Computation of the SCR Circuits

In the digital computation of the systems containing SCR circuits there arise generally two problems. One of them is the accuracy of the mathematical model used for the representation of the characteristics of the silicon switching element. The other one is the difficulty in the numerical intiegration of the state equations which have usually widely separated time-constants. Using a modified model for SCR elements this paper has adopted the stiffly stable algorithm, given by Gear (1), in the digital computation of the SCR circuits, and it is shown that the numerical integration problem can be solved without any fictitious components or changing the structure of the system.