A Two-Phase Algorithm for the Chebyshev Solution of Complex Linear Equations

1994 ◽  
Vol 15 (6) ◽  
pp. 1440-1451
Author(s):  
Dirk P. Laurie ◽  
Lucas M. Venter
Keyword(s):  
Linear Equations ◽  
Two Phase ◽  
Complex Linear

Wavy Motion of Viscous Bubbly Liquid in Tubes of Orthotropic Material

2012 ◽  
Vol 2 (1) ◽  
pp. 39-47
Author(s):  
Rafael Yusif Amenzadeh ◽  
Akperli Reyhan Sayyad ◽  
Faig Bakhman Ogli Naghiyev
Keyword(s):  
Orthotropic Material ◽  
Volume Fraction ◽  
Linear Equations ◽  
Bubbly Liquid ◽  
Air Bubbles ◽  
Two Phase ◽  
One Dimensional ◽  
Wave Characteristics ◽  
Infinite Tube ◽  
Limited Process

This article investigates the pulsating flow of a compressible two-phase bubble of viscous fluid contained in an elastic orthotropicle direct axis tube. In this work, one-dimensional linear equations have been used. It is assumed that the tube is rigidly attached to the certain environment. In the case of finite length the pressure is applied at the end of its faces. In the limited process, relations obtained for a very long tube. Such a description, in a sense generalizes and strengthens the work of this type. In the numerical experiment a semi-infinite tube with flowing water containing small amount of air bubbles is considered. The influence of volume fraction of bubbles on wave characteristics is determined.

scholarly journals A general existence result for isothermal two-phase flows with phase transition

2019 ◽  
Vol 16 (04) ◽  
pp. 595-637
Author(s):  
Maren Hantke ◽  
Ferdinand Thein
Keyword(s):  
Phase Transition ◽  
Euler Equations ◽  
Equations Of State ◽  
Linear Equations ◽  
Two Phase Flows ◽  
Kinetic Relation ◽  
Two Phase ◽  
Uniqueness Results ◽  
Wide Range ◽  
Isothermal Euler Equations

Liquid–vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations, where the mass transfer is modeled by a kinetic relation, have been investigated analytically in [M. Hantke, W. Dreyer and G. Warnecke, Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition, Quart. Appl. Math. 71(3) (2013) 509–540]. This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of this work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and cavitation are discussed.

Advanced Numerical Methods for the Prediction of Tonal Noise in Turbomachinery—Part II: Time-Linearized Methods

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken ◽  
Christian Weckmüller
Keyword(s):  
Boundary Condition ◽  
Linear System ◽  
Near Field ◽  
Linear Equations ◽  
Time Integration ◽  
Aerodynamic Noise ◽  
Fan Noise ◽  
Rotor Stator Interaction ◽  
Complex Linear ◽  
Computational Fluid Dynamics Cfd

This is the second part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. It focuses on the application of linearized RANS methods to turbomachinery noise problems. The convective and viscous fluxes of an existing URANS solver are linearized and the resulting unsteady linear equations are transferred into the frequency domain, thereby simplifying the solution problem from unsteady time-integration to a complex linear system. The linear system is solved using a parallel, preconditioned general minimized residual (GMRES) method with restarts. In order to prescribe disturbances due to rotor stator interaction, a so-called gust boundary condition is implemented. Using this inhomogeneous boundary condition, one can compute the generation of the acoustic modes and their near field propagation. The application of the time-linearized methods to a modern high-bypass ratio fan is investigated. The tonal fan noise predicted by the time-linearized solver is compared to numerical results presented in the first part and to measurements.

Network models for two-phase flow in porous media Part 1. Immiscible microdisplacement of non-wetting fluids

1986 ◽  
Vol 164 ◽  
pp. 305-336 ◽  
Author(s):  
Madalena M. Dias ◽  
Alkiviades C. Payatakes
Keyword(s):  
Porous Medium ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Linear Equations ◽  
Small Time ◽  
Creeping Flow ◽  
Flow In Porous Media ◽  
Two Phase ◽  
Unit Cells ◽  
Wetting Fluid

A theoretical simulator of immiscible displacement of a non-wetting fluid by a wetting one in a random porous medium is developed. The porous medium is modelled as a network of randomly sized unit cells of the constricted-tube type. Under creeping-flow conditions the problem is reduced to a system of linear equations, the solution of which gives the instantaneous pressures at the nodes and the corresponding flowrates through the unit cells. The pattern and rate of the displacement are obtained by assuming quasi-static flow and taking small time increments. The porous medium adopted for the simulations is a sandpack with porosity 0.395 and grain sizes in the range from 74 to 148 μrn. The effects of the capillary number, Ca, and the viscosity ratio, κ = μo/μw, are studied. The results confirm the importance of the capillary number for displacement, but they also show that for moderate and high Ca values the role of κ is pivotal. When the viscosity ratio is favourable (κ < 1), the microdisplacement efficiency begins to increase rapidly with increasing capillary number for Ca > 10−5, and becomes excellent as Ca → 10−3. On the other hand, when the viscosity ratio is unfavourable (κ > 1), the microdisplacement efficiency begins to improve only for Ca values larger than, say, 5 × 10−4, and is substantially inferior to that achieved with κ < 1 and the same Ca value. In addition to the residual saturation of the non-wetting fluid, the simulator predicts the time required for the displacement, the pattern of the transition zone, the size distribution of the entrapped ganglia, and the acceptance fraction as functions of Ca, κ, and the porous-medium geometry.

FUZZY CENTRE BASED SOLUTION OF FUZZY COMPLEX LINEAR SYSTEM OF EQUATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 629-642 ◽  
Author(s):  
DIPTIRANJAN BEHERA ◽  
S. CHAKRAVERTY
Keyword(s):  
Linear Time ◽  
Linear Equations ◽  
Electric Circuit ◽  
System Of Linear Equations ◽  
New Approach ◽  
Linear System Of Equations ◽  
Linear Time Invariant ◽  
Complex Linear ◽  
Time Invariant ◽  
Good Agreement

A new approach to solve Fuzzy Complex System of Linear Equations (FCSLE) based on fuzzy complex centre procedure is presented here. Few theorems related to the investigation are stated and proved. Finally the presented procedure is used to analyze an example problem of linear time invariant electric circuit with complex crisp coefficient and fuzzy complex sources. The results obtained are also compared with the known solutions and are found to be in good agreement.

Propagation of Longitudinal Waves in Circularly Cylindrical Bone Elements

1971 ◽  
Vol 38 (3) ◽  
pp. 578-584 ◽  
Author(s):  
J. L. Nowinski ◽  
C. F. Davis
Keyword(s):  
Linear Equations ◽  
Elastic Solid ◽  
Variable Coefficients ◽  
External Loading ◽  
Regular Singular Point ◽  
Two Phase ◽  
Longitudinal Waves ◽  
Living Bone ◽  
Poroelastic Material ◽  
Biot’S Equations

Two-phase poroelastic material is taken as a model of the living bone in the sense that the osseous tissue is treated as a linear isotropic perfectly elastic solid, and the fluid substances filling the pores as a perfect fluid. Using Biot’s equations, derived in his consolidation theory, four coupled governing differential equations for the propagation of harmonic longitudinal waves in circularly cylindrical bars of poroelastic material are derived. A longer manipulation reduces the task of solution to a single ordinary differential equation with variable coefficients and a regular singular point. The equation is solved by Frobenius’ method. Three boundary conditions on the curved surface of the bar, expressing the absence of external loading and the permeability of the surface, supply a system of three linear equations in three unknown coefficients. A nontrivial solution of the system gives two phase velocities of propagation of longitudinal waves in agreement with the finding of Biot for an infinite medium. A simplification to the purely elastic case yields the elementary classical result for the longitudinal waves.

Comprehensive study on complex-valued ZNN models activated by novel nonlinear functions for dynamic complex linear equations

2021 ◽  
Vol 561 ◽  
pp. 101-114
Author(s):  
Jianhua Dai ◽  
Yiwei Li ◽  
Lin Xiao ◽  
Lei Jia ◽  
Qing Liao ◽  
...  
Keyword(s):  
Linear Equations ◽  
Nonlinear Functions ◽  
Complex Linear ◽  
Complex Valued ◽  
Comprehensive Study

scholarly journals Exciting Fixed Point Results on a Novel Space with Supportive Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hasanen A. Hammad ◽  
Hassen Aydi ◽  
Yaé Ulrich Gaba
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Metric Spaces ◽  
Linear Equations ◽  
Topological Properties ◽  
Rlc Circuit ◽  
Complex Linear ◽  
New Space ◽  
Complex Valued ◽  
Theoretical Results

The goal of this paper is to present a new space, a complex valued controlled rectangular b -metric space (for short, υ ℂ -metric space). Some examples and topological properties of υ ℂ -metric spaces are given. Also, some related common fixed point results are discussed. Our results generalize a lot of works in this direction. Moreover, we apply the theoretical results to find a unique solution of a complex valued Atangana-Baleanu fractional integral operator and a system of complex linear equations. Finally, a numerical example to find the current that passes through the RLC circuit is illustrated.

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