scholarly journals Approximation of potential-driven flow dynamics in large-scale self-similar tree networks

2011 ◽  
Vol 467 (2134) ◽  
pp. 2810-2824 ◽  
Author(s):  
Jason Mayes ◽  
Mihir Sen
Keyword(s):  
Mathematical Model ◽  
Analytical Solutions ◽  
Large Scale ◽  
Differential Algebraic Equations ◽  
Flow Dynamics ◽  
Algebraic Equations ◽  
Tree Networks ◽  
Self Similar ◽  
Large Scale Flow ◽  
The Mathematical Model

Dynamic analysis of large-scale flow networks is made difficult by the large system of differential-algebraic equations resulting from its modelling. To simplify analysis, the mathematical model must be sufficiently reduced in complexity. For self-similar tree networks, this reduction can be made using the network’s structure in way that can allow simple, analytical solutions. For very large, but finite, networks, analytical solutions are more difficult to obtain. In the infinite limit, however, analysis is sometimes greatly simplified. It is shown that approximating large finite networks as infinite not only simplifies the analysis, but also provides an excellent approximate solution.

scholarly journals МАТЕМАТИЧЕСКАЯ МОДЕЛЬ ТОПЛИВНОГО НАСОСА-РЕГУЛЯТОРА ТУРБОВАЛЬНОГО ДВИГАТЕЛЯ ВЕРТОЛЕТА

2020 ◽  
pp. 105-112
Author(s):  
Игорь Валериевич Оганян
Keyword(s):  
Mathematical Model ◽  
Differential Algebraic Equations ◽  
Diagnostic Methods ◽  
Working Fluid ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Technical Documentation ◽  
Technical Specifications ◽  
Lumped Parameters ◽  
The Mathematical Model

This article discusses the relevance of creating a mathematical model of a hydromechanical fuel regulator as the main component of the parametric diagnostics method. To understand the processes occurring during the operation of the fuel regulator, this article provides a brief description of its operation. Based on the problems solved by the diagnostic methods and the features of the fuel regulator, the basic requirements for its mathematical model are formulated and the structure of this model is determined. Several assumptions are made (one-dimensional flow of the working fluid and its zero thermal conductivity), which make it possible to significantly simplify the structure of the model and the number of simulated parameters. The mathematical model consists of idealized elements with lumped parameters (such as pressure and flow rate of the working fluid), takes into account the compressibility of the working fluid, as well as the design features of the regulator (mechanical stops, complex profiled dosing windows of spools, relay-type switches). As an example, this article contains equations for the elements with lumped parameters, interconnected by hydraulic channels in one node. The compiled mathematical model is a system of differential-algebraic equations of the first index. To solve such a system, a special implicit solver is used. The calculation of the parameters of the mathematical model for static and transient operating modes of the fuel regulator has been made. The results of calculating the model parameters in various modes are compared with the requirements for these parameters set in the technical specifications for the simulated fuel regulator. The correspondence of the calculated parameters to the values specified in the technical documentation was ensured by the selection of input parameters (tightening of springs of elastic elements, area of throttling elements, etc.). From the results obtained, it was concluded that the model makes it possible to diagnose the technical state of the fuel regulator at the stages of adjustment during production and repair, as well as at the stage of its operation.

Reactive Extraction Using Moving Liquid Membranes - Mathematical Model Calibration Through Experiments

2017 ◽  
Vol 68 (10) ◽  
pp. 2293-2306
Author(s):  
Daniel Dumitru Dinculescu ◽  
Cristiana Luminita Gijiu ◽  
Vasile Lavric
Keyword(s):  
Mathematical Model ◽  
Organic Liquid ◽  
Extraction Process ◽  
Differential Algebraic Equations ◽  
Reactive Extraction ◽  
Algebraic Equations ◽  
Orthogonal Collocation ◽  
Type Method ◽  
The Mathematical Model ◽  
Moving Liquid

A reactive extraction/back-extraction process was studied experimentally in a two-stage column. The mathematical model of the reactive extraction using a closed loop moving organic liquid membrane, based upon first principle equations, was derived as a set of Partial/Ordinary Differential Algebraic Equations (P/ODAE). The mathematical model, reduced through orthogonal collocation to a system of ODAE, was solved using a self-adaptive Runge-Kutta (RK)-type method. The mathematical model was calibrated using own batch experimental data and a modified genetic algorithm as optimizer.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

2021 ◽  
pp. 43-54
Author(s):  
A. N. Krutov ◽  
◽  
S. Ya. Shkol’nikov ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Wave Equations ◽  
Simple Wave ◽  
Kinematic Wave ◽  
Calculation Results ◽  
Self Similar ◽  
Similar Solutions ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

scholarly journals A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1174 ◽  
Author(s):  
Yutaka Okabe ◽  
Akira Shudo
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Sir Model ◽  
Exact Analytical Solutions ◽  
The Mathematical Model ◽  
Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

Features of mathematical modeling of wood-polymer composite sandy

10.12737/8462 ◽  
2015 ◽  
Vol 4 (4) ◽  
pp. 130-139
Author(s):  
Стародубцева ◽  
Tamara Starodubtseva ◽  
Аскомитный ◽  
Aleksey Askomitnyy
Keyword(s):  
Mathematical Modeling ◽  
Mechanical Properties ◽  
Mathematical Model ◽  
Initial Data ◽  
Algebraic Equations ◽  
Wood Polymer ◽  
Composite Interface ◽  
Input Form ◽  
The Mathematical Model ◽  
Wood Polymer Composite

This article describes a technique for modeling of wood polymer-sandy composite. Interface input form of initial data for modeling; differential equations underlying the mathematical model are presented. To solve the system of differential and algebraic equations computer program "Program to simulate the struc-ture and mechanical properties of wood polymer-sandy composite" is developed. The program, developed in the environment of Borland Delphi 7.0, programming language Object Pascal, is intended for modeling the mechanical behavior of wood polymer-sandy composite of given composition.

Pointwise Optimal Control of Dynamical Systems Described by Constrained Coordinates

1999 ◽  
Vol 121 (4) ◽  
pp. 594-598 ◽  
Author(s):  
V. Radisavljevic ◽  
H. Baruh
Keyword(s):  
Optimal Control ◽  
Dynamical Systems ◽  
Feedback Control ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Control Law ◽  
Algebraic Equations ◽  
The Stability ◽  
The Mathematical Model

A feedback control law is developed for dynamical systems described by constrained generalized coordinates. For certain complex dynamical systems, it is more desirable to develop the mathematical model using more general coordinates then degrees of freedom which leads to differential-algebraic equations of motion. Research in the last few decades has led to several advances in the treatment and in obtaining the solution of differential-algebraic equations. We take advantage of these advances and introduce the differential-algebraic equations and dependent generalized coordinate formulation to control. A tracking feedback control law is designed based on a pointwise-optimal formulation. The stability of pointwise optimal control law is examined.

The Numerical Simulation of Directional Solidification Process Temperature Field for Large-Scale Frustum of a Cone Ingot

2011 ◽  
Vol 189-193 ◽  
pp. 1476-1481
Author(s):  
Kun Liu ◽  
Zhe Wang ◽  
Ren Zhi Han ◽  
Zi Ping Ren
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Temperature Field ◽  
Directional Solidification ◽  
Large Scale ◽  
Solidification Process ◽  
Directional Solidification Process ◽  
Ingot Quality ◽  
Fluent Software ◽  
The Mathematical Model

By using Fluent software, the mathematical model of temperature field is established on directional solidification process for large-scale frustum of a cone ingot, and the result is analyzed by Origin software, Tecplot. The influences of different width/thickness ratio to directional solidification process of cone ingot are discussed in order to provide basis for design optimization and ingot quality improvement.

On the Numerical Scheme to Solve a Realistic Chemical Vapor Infiltration Reactor Model

2007 ◽  
Author(s):  
John K. Kamel ◽  
Samuel Paolucci
Keyword(s):  
Mathematical Model ◽  
Numerical Integration ◽  
Chemical Vapor ◽  
Differential Algebraic Equations ◽  
Chemical Vapor Infiltration ◽  
Integration Scheme ◽  
Algebraic Equations ◽  
Splitting Algorithm ◽  
Reactor Model ◽  
Vapor Infiltration

We describe the general mathematical model as well as the numerical integration procedure arising in modeling a realistic chemical vapor infiltration process. The numerical solution of the model ultimately leads to the solution of a large system of stiff differential algebraic equations. An operator splitting algorithm is employed to overcome the stiffness associated with chemical reactions, whereas a projection method is employed to overcome the difficulty arising from having to solve a large coupled system for the velocity and pressure fields. The resulting mathematical model and the numerical integration scheme are used to explore temperature, velocity, and concentration fields inside a chemical vapor infiltration reactor used in the manufacturing of aircraft brakes.

Large-scale flow in turbulent convection: a mathematical model

1986 ◽  
Vol 170 ◽  
pp. 385-410 ◽  
Author(s):  
L. N. Howard ◽  
R. Krishnamurti
Keyword(s):  
Mathematical Model ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Boussinesq Equations ◽  
Time Dependent ◽  
Heteroclinic Orbits ◽  
Turbulent Convection ◽  
Mean Flow ◽  
Dependent Flow ◽  
Large Scale Flow

A mathematical model of convection, obtained by truncation from the two-dimensional Boussinesq equations, is shown to exhibit a bifurcation from symmetrical cells to tilted non-symmetrical ones. A subsequent bifurcation leads to time-dependent flow with similarly tilted transient plumes and a large-scale Lagrangian mean flow. This change of symmetry is similar to that occurring with the advent of a large-scale flow and transient tilted plumes seen in laboratory experiments on turbulent convection at high Rayleigh number. Though not intended as a description of turbulent convection, the model does bring out in a theoretically tractable context the possibility of the spontaneous change of symmetry suggested by the experiments.Further bifurcations of the model lead to stable chaotic phenomena as well. These are numerically found to occur in association with heteroclinic orbits. Some mathematical results clarifying this association are also presented.

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