• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.60.6-61
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• 2008

• 한국전산유체공학회:학술대회논문집
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• 2008.08a
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• pp.53.3-53.3
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• 2008

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.63-65
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• 2006

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.333-334
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• 2006

• Journal of computational fluids engineering
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• v.10 no.1
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• pp.99-106
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• 2005

Performance of first, second and third order accurate methods for calculation of in viscid fluxes in fluid flow governing equations are investigated here. For the purpose, an upwind method based on Roe's scheme is used to solve 2-dimensional Euler equations. To increase the accuracy of the method two different schemes are applied. The first one is a second and third order upwind-based algorithm with the MUSCL extrapolation Van Leer (1979), based on primitive variables. The other one is an upwind-based algorithm with the Chakravarthy extrapolation to the fluxes of mass, momentum and energy. The results show that the thickness of shock layer in the third order accuracy is less than its value in second order. Moreover, applying limiter eliminates the oscillations near the shock while increases the thickness of shock layer especially in MUSCL method using Van Albada limiter.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Journal of computational fluids engineering
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• v.4 no.3
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• pp.21-27
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• 1999

In this paper, tile characteristics of flow resulting from the configurations of piston head and intake-port of the cylinder in a gasoline-direct-injection engine are investigated numerically. Calculations are carried out from intake process to the end of compression. GTT code which includes the third order upwind Chakravarthy-Osher TVD scheme and κ-ε turbulence model with the law of wall as a boundary condition. As a result, a piston head with a smaller radius of curvature and larger radius gives stronger reverse tumble. It is also shown that as the maximum tumble ratio increases by the configuration of the intake-port the tumble ratio at the end of compression stroke increases. It is concluded that flows at the end of compression stroke can be controlled by the optimum design of intake-port and piston head.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.351-373
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• 2020

There is an extensive literature on retrial queueing models. While a majority of the literature on retrial queueing models focuses on the retrial times to be exponentially distributed (so as to keep the state space to be of a reasonable size), a few papers deal with nonexponential retrial times but with some additional restrictions such as constant retrial rate, only the customer at the head of the retrial queue will attempt to capture a free server, 2-state phase type distribution, and finite retrial orbit. Generally, the retrial queueing models are analyzed as level-dependent queues and hence one has to use some type of a truncation method in performing the analysis of the model. In this paper we study a retrial queueing model with threshold-type policy for orbiting customers in the context of nonexponential retrial times. Using matrix-analytic methods we analyze the model and compare with the classical retrial queueing model through a few illustrative numerical examples. We also compare numerically our threshold retrial queueing model with a previously published retrial queueing model that uses a truncation method.