Group theoretic and similarity analysis of hyperbolic partial differential equations

Frydrychowicz, W.; Singh, M. C.

doi:10.1016/0022-247x(86)90067-3

Cited by 13 publications

(3 citation statements)

References 10 publications

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“…The problem (4.1) describes a shock front propagation in a constant state. The shock front propagation into the known state ahead of the shock is due to the time dependent stress impact at the end of the thin rod (Taulbee, Cozzarelli, and Dym [72], Singh and Frydrychowicz [70], Fusco [41], and Frydrychowicz and Singh [40]). The given moving boundary conditions are the Rankine-Hugoniot conditions at the shock.…”

Section: Applications (With Numerical Results)mentioning

confidence: 99%

“…In recent years a great deal of attention has been devoted to apply the similarity analysis to impact problems in nonlinear elasticity (see Taulbee, Cozzarelli, and Dym [72], Singh and Frydrychowicz [69], Singh and Frydrychowicz [70], Dresner [20, pp. 77-87], Frydrychowicz and Singh [40], Donato [18], Fazio [28], and Fazio and Evans [38]). Moreover, the relevance of models describing the evolution of a shock at the initial time cannot be underestimated.…”

Section: Discussionmentioning

confidence: 99%

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A Similarity Approach to the Numerical Solution of Free Boundary Problems

Fazio¹

1998

SIAM Rev.

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The aim of this work is to point out that within a similarity approach some classes of free boundary value problems governed by ordinary differential equations can be transformed to initial value problems. The interest in the numerical solution of free boundary problems arises because these are always nonlinear problems. Furthermore we show that free boundary problems arise also via a similarity analysis of moving boundary hyperbolic problems and they can be obtained as approximations of boundary value problems defined on infinite intervals. Most of the theoretical content of this survey is original: it generalizes and unifies results already available in literature. As far as applications of the proposed approach are concerned, three problems of interest are considered and numerical results for each of them are reported.

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Section: Applications (With Numerical Results)mentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A Similarity Approach to the Numerical Solution of Free Boundary Problems

Fazio¹

1998

SIAM Rev.

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“…For similarity analysis, Moran and Gaggioli [1] developed systematic group formalism. A quasi-linear hyperbolic second order PDE was analysed by Frydrychowicz and Singh [2] in their research to shows that conformal invariance of PDE's under multiparameter-dimensional group transformation implied the conformal in-variance of its characteristics. Heat transfer and fluid flow characteristics were studied by Abd-El-Malek and Badran [3] for unsteady and steady surfaces respectively, by analysing the free laminar convection on a circular vertical cylinder applying the Group Method.…”

Section: Introductionmentioning

confidence: 99%

Group Method of Uniform Surface Heat Flux from a Vertical Cone Using Laminar Free Convection

Maheshwaran¹,

Pullepu²,

Pinelas³

2023

MMEP

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In this study, the Group Transformation method is employed to simulate the laminar free convection problem involving a viscous incompressible fluid on a vertically oriented cone with a uniform heat flux on its surface. The non-dimensional governing partial differential equations (PDEs) and their boundary conditions are reduced to ordinary differential equations (ODEs) with corresponding appropriate conditions. To solve the resulting non-linear ODEs, the Range-Kutta shooting method is applied. The temperature and velocity fields are graphically presented for various parameters, such as the semi-vertical angle and Prandtl number. Furthermore, the local Nusselt number and skin fraction are analyzed numerically.

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Similarity and Numerical Analysis of a Singular Moving Boundary Hyperbolic Problem

Fazio

2002

Progress in Industrial Mathematics at ECMI 2000

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Group theoretic and similarity analysis of hyperbolic partial differential equations

Cited by 13 publications

References 10 publications

A Similarity Approach to the Numerical Solution of Free Boundary Problems

A Similarity Approach to the Numerical Solution of Free Boundary Problems

Group Method of Uniform Surface Heat Flux from a Vertical Cone Using Laminar Free Convection

Similarity and Numerical Analysis of a Singular Moving Boundary Hyperbolic Problem

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