scholarly journals A Galerkin Method for a Gaseous Ignition Model

2012 ◽  
Vol 17 (2) ◽  
pp. 224
Author(s):  
M. Salman ◽  
Jintae Kim
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Integrodifferential Equation ◽  
Order Of Convergence ◽  
Combustion Model ◽  
Gas Combustion ◽  
Galerkin Procedure ◽  
Variational Form ◽  
The Given ◽  
Crank Nicolson

We consider a Galerkin procedure to solve a parabolic integrodifferential equation that arises in a gas combustion model. This model has been proposed by Kassoy and Poland, and subsequently analyzed by Bebernes, Eberly and Bressan. The problem is formulated in the variational form. In order to estimate the error, some intermediate projection has been employed. Under certain conditions on the given data, the error estimate has been obtained. A fully descretized version by using an extrapolated Crank-Nicolson method has been applied and the order of convergence  derived.  

Design Analysis of a Micro Gas Turbine Combustion Chamber Burning Natural Gas

2012 ◽  
Author(s):  
André Perpignan V. de Campos ◽  
Fernando L. Sacomano Filho ◽  
Guenther C. Krieger Filho
Keyword(s):  
Experimental Data ◽  
Natural Gas ◽  
Combustion Chamber ◽  
Gas Turbines ◽  
Low Cost ◽  
Mixture Fraction ◽  
Combustion Model ◽  
Inlet Temperature ◽  
Gas Combustion ◽  
Micro Turbine

Gas turbines are reliable energy conversion systems since they are able to operate with variable fuels and independently from seasonal natural changes. Within that reality, micro gas turbines have been increasing the importance of its usage on the onsite generation. Comparatively, less research has been done, leaving more room for improvements in this class of gas turbines. Focusing on the study of a flexible micro turbine set, this work is part of the development of a low cost electric generation micro turbine, which is capable of burning natural gas, LPG and ethanol. It is composed of an originally automotive turbocompressor, a combustion chamber specifically designed for this application, as well as a single stage axial power turbine. The combustion chamber is a reversed flow type and has a swirl stabilized combustor. This paper is dedicated to the diagnosis of the natural gas combustion in this chamber using computational fluid dynamics techniques compared to measured experimental data of temperature inside the combustion chamber. The study emphasizes the near inner wall temperature, turbine inlet temperature and dilution holes effectiveness. The calculation was conducted with the Reynolds Stress turbulence model coupled with the conventional β-PDF equilibrium along with mixture fraction transport combustion model. Thermal radiation was also considered. Reasonable agreement between experimental data and computational simulations was achieved, providing confidence on the phenomena observed on the simulations, which enabled the design improvement suggestions and analysis included in this work.

An L∞-error Estimate for the h-p Version Continuous Petrov-Galerkin Method for Nonlinear Initial Value Problems

2015 ◽  
Vol 5 (4) ◽  
pp. 301-311 ◽  
Author(s):  
Lijun Yi
Keyword(s):  
Error Estimate ◽  
Galerkin Method ◽  
Error Bound ◽  
Initial Value Problems ◽  
Initial Value ◽  
Numerical Examples ◽  
Time Stepping ◽  
Theoretical Results

AbstractThe h-p version of the continuous Petrov-Galerkin time stepping method is analyzed for nonlinear initial value problems. An L∞-error bound explicit with respect to the local discretization and regularity parameters is derived. Numerical examples are provided to illustrate the theoretical results.

scholarly journals A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Fourth Order ◽  
Order Of Convergence ◽  
Nonsmooth Equations ◽  
Order Convergence ◽  
Linear Combinations ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Seventh Order ◽  
The Given

A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.6266. Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.

scholarly journals Computational Sinc-scheme for extracting analytical solution for the model Kuramoto-Sivashinsky equation

2019 ◽  
Vol 9 (5) ◽  
pp. 3720
Author(s):  
Kamel Al-Khaled ◽  
Issam Abu-Irwaq
Keyword(s):  
Analytical Solution ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Present Article ◽  
Point Theory ◽  
Algebraic Equations ◽  
Time Direction ◽  
Numerical Examples ◽  
Sivashinsky Equation ◽  
Crank Nicolson

The present article is designed to supply two different numerical<br />solutions for solving  Kuramoto-Sivashinsky equation. We have made<br />an attempt to develop a numerical solution via the use of<br />Sinc-Galerkin method for  Kuramoto-Sivashinsky equation, Sinc<br />approximations to both derivatives and indefinite integrals reduce<br />the solution to an explicit system of algebraic equations. The fixed<br />point theory is used to prove the convergence of the proposed<br />methods. For comparison purposes, a combination of a Crank-Nicolson<br />formula in the time direction, with the Sinc-collocation in the<br />space direction is presented, where the derivatives in the space<br />variable are replaced by the necessary matrices to produce a system<br />of algebraic equations. In addition, we present numerical examples<br />and comparisons to support the validity of these proposed<br />methods.

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