3D Goursat Problem in the Non-Classical Treatment for Manjeron Generalized Equation with Non-Smooth Coefficients
Ilgar Gurbat oglu Mamedov
Issue:
Volume 4, Issue 1-1, January 2015
Pages:
1-5
Received:
21 April 2014
Accepted:
22 June 2014
Published:
30 June 2014
DOI:
10.11648/j.acm.s.2015040101.11
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Abstract: In this paper substantiated for a Manjeron generalized equation with non-smooth coefficients a three dimensional Goursat problem -3D Goursat problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions three dimensional boundary condition is substantiated classical, in the case if the solution of the problem in the isotropic S. L. Sobolev's space is found. The considered equation as a hyperbolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (telegraph equation, Aller's equation, moisture transfer generalized equation, Manjeron equation, Boussinesq - Love equation and etc.). It is grounded that the 3D Goursat boundary conditions in the classic and non-classic treatment are equivalent to each other. Thus, namely in this paper, the non-classic problem with 3D Goursat conditions is grounded for a hyperbolic equation of sixth order. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev isotropic space.W_p^((2,2,2) ) (G)
Abstract: In this paper substantiated for a Manjeron generalized equation with non-smooth coefficients a three dimensional Goursat problem -3D Goursat problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions three dimensional boundary condition is substantiated classical, in the case...
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Implicit Runge-Kutta Method for Van Der Pol Problem
Jafar Biazar,
Meysam Navidyan
Issue:
Volume 4, Issue 1-1, January 2015
Pages:
6-11
Received:
7 June 2014
Accepted:
25 June 2014
Published:
13 July 2014
DOI:
10.11648/j.acm.s.2015040101.12
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Abstract: In this manuscript the implicit Runge-Kutta (IRK) method, with three slopes of order five has been explained, and is applied to Van der pol stiff differential equation. Truncation error, of order five, has been estimated. Stability of the procedure for the Van der pol equation, is analyzed by the Lyapunov method. To illustrate the structure of the method, an Algorithm is presented to solve this stiff problem. Results confirm the validity and the ability of this approach.
Abstract: In this manuscript the implicit Runge-Kutta (IRK) method, with three slopes of order five has been explained, and is applied to Van der pol stiff differential equation. Truncation error, of order five, has been estimated. Stability of the procedure for the Van der pol equation, is analyzed by the Lyapunov method. To illustrate the structure of the...
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Comparison between Finite Volume Method (FVM) Based on Inviscid and Viscous Flow with Experimental and Fluent Results
Abobaker Mohammed Alakashi,
Bambang Basuno,
Hasan Taher. M. Elkamel
Issue:
Volume 4, Issue 1-1, January 2015
Pages:
12-17
Received:
4 January 2015
Accepted:
26 January 2015
Published:
9 February 2015
DOI:
10.11648/j.acm.s.2015040101.13
Downloads:
Views:
Abstract: The Finite Volume Method (FVM) is currently the most popular method in CFD. The main reason is that it can resolve some of the difficulties that the other methods have. Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems [1]. Finite volume method can be classified into three groups: (1) Cell-centered scheme, (2) Cell-vertex scheme with overlapping control volumes and (3), Cell-vertex scheme with dual control volumes [2]. The present work used Finite volume based Cell Cell-centered. This approach used the grid cell identical to its control volume. While in view of a manner the grid cells in this work can be defined numerically, it can follow as a structured grid based on Elliptic grid generation PDEs [3]. Computer code had been developed by using a cell centered Finite volume scheme combined with structured grid approach. The computer codes applied for the case of compressible flow past through an airfoil NACA 0012, in which the flow problem can be treated as purely inviscid flow or as the flow with viscous effect but considered to be as a laminar flow. The comparison result presented in term of pressure coefficient Cp for different angle of attack using available experimental result and the result provided by Fluent software. In term for the case of flow problem treated as an inviscid flow, both the developed computer code and Fluent software produce the result closed to the experimental result. However if the developed computer code as well as fluent software treated the flow problem to include the viscous effect by considering them as a laminar flow both are slightly deviate with the experimental results. Strictly speaking the present developed computer code give a similar result as the experimental result, which both showing that this type of airfoil having a sensitive effect to the angle of attack. A small change of angle of attack will produce a significant change to the location of shock will occurred.
Abstract: The Finite Volume Method (FVM) is currently the most popular method in CFD. The main reason is that it can resolve some of the difficulties that the other methods have. Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems [1]. Finit...
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