Solution of Variable Coefficients PDEs by Means of BEM and Perturbation Technique

1991 ◽  
pp. 99-108
Author(s):  
R. Rangogni
Keyword(s):  
Perturbation Technique ◽  
Variable Coefficients

scholarly journals Analytical model of reactive transport processes with spatially variable coefficients

2015 ◽  
Vol 2 (5) ◽  
pp. 140348 ◽  
Author(s):  
Matthew J. Simpson ◽  
Liam C. Morrow
Keyword(s):  
Reactive Transport ◽  
Initial Conditions ◽  
Perturbation Technique ◽  
Variable Coefficients ◽  
Transport Processes ◽  
Screening Tools ◽  
Analytical Models ◽  
Solution Technique ◽  
Regular Perturbation ◽  
Contaminant Fate And Transport

Analytical solutions of partial differential equation (PDE) models describing reactive transport phenomena in saturated porous media are often used as screening tools to provide insight into contaminant fate and transport processes. While many practical modelling scenarios involve spatially variable coefficients, such as spatially variable flow velocity, v ( x ), or spatially variable decay rate, k ( x ), most analytical models deal with constant coefficients. Here we present a framework for constructing exact solutions of PDE models of reactive transport. Our approach is relevant for advection-dominant problems, and is based on a regular perturbation technique. We present a description of the solution technique for a range of one-dimensional scenarios involving constant and variable coefficients, and we show that the solutions compare well with numerical approximations. Our general approach applies to a range of initial conditions and various forms of v ( x ) and k ( x ). Instead of simply documenting specific solutions for particular cases, we present a symbolic worksheet, as supplementary material, which enables the solution to be evaluated for different choices of the initial condition, v ( x ) and k ( x ). We also discuss how the technique generalizes to apply to models of coupled multispecies reactive transport as well as higher dimensional problems.

Usefulness of Foundry Tooling Materials in Microwave Heating Process

2013 ◽  
Vol 58 (3) ◽  
pp. 919-922 ◽  
Author(s):  
K. Granat ◽  
B. Opyd ◽  
D. Nowak ◽  
M. Stachowicz ◽  
G. Jaworski
Keyword(s):  
Electromagnetic Field ◽  
Microwave Heating ◽  
Loss Factor ◽  
Perturbation Technique ◽  
Resonant Cavity ◽  
Precise Determination ◽  
Heating Process ◽  
Basic Criterion ◽  
Measurement Results ◽  
Heating Technology

Abstract The paper describes preliminary examinations on establishing usefulness criteria of foundry tooling materials in the microwave heating technology. Presented are measurement results of permittivity and loss tangent that determine behaviour of the materials in electromagnetic field. The measurements were carried-out in a waveguide resonant cavity that permits precise determination the above-mentioned parameters by perturbation technique. Examined were five different materials designed for use in foundry tooling. Determined was the loss factor that permits evaluating usefulness of materials in microwave heating technology. It was demonstrated that the selected plastics meet the basic criterion that is transparency for electromagnetic radiation.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

Slip And Hall Effects On The Flow Of A Hyperbolic Tangent Fluid Through Porous Medium In A Planar Channel With Peristalsis

GIS Business ◽  
2020 ◽  
Vol 15 (1) ◽  
pp. 383-394
Author(s):  
K. Shalini ◽  
K.Rajasekhar
Keyword(s):  
Porous Medium ◽  
Pressure Gradient ◽  
Volume Flow Rate ◽  
Perturbation Technique ◽  
Volume Flow ◽  
Planar Channel ◽  
Hyperbolic Tangent ◽  
Closed Form Solutions ◽  
Long Wavelength ◽  
Hall Effects

In this paper, the effect of Slip and Hall effects on the flow of Hyperbolic tangent fluid through a porous medium in a planar channel with peristalsis under the assumption of long wavelength is investigated. A Closed form solutions are obtained for axial velocity and pressure gradient by employing perturbation technique. The effects of various emerging parameters on the pressure gradient, time averaged volume flow rate and frictional force are discussed with the aid of graphs.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

Designing Experiments for Model Identification of the Nitrification Process

1991 ◽  
Vol 24 (6) ◽  
pp. 9-16 ◽  
Author(s):  
P. J. Ossenbruggen ◽  
H. Spanjers ◽  
H. Aspegren ◽  
A. Klapwijk
Keyword(s):  
Mechanistic Model ◽  
Nonlinear Differential Equations ◽  
Model Identification ◽  
Reaction Rates ◽  
Variable Coefficients ◽  
Model Specification ◽  
First Order ◽  
Interactive Behavior ◽  
Batch Tests ◽  
Nitrification Process

A series of batch tests were performed to study the competition for oxygen by Nitrosomonas and Nitrobacter in the nitrification of ammonia in activated sludge. Oxygen uptake rate (OUR) and dynamic (compartment) models describing the process are proposed and tested. The OUR model is described by a Monod relationship and the biogradation process by a set of first order nonlinear differential equations with variable coefficients. The results show a mechanistic model and ten reaction rates are sufficient to capture the interactive behavior of the nitrification process. Methods for model specification, calibrating, and testing the model and the design of additional experiments are described.

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