A Meshless Semi-Analytical Method for Solving Convection Problems in Complex-Shaped Closed Cavities

Mikhail Basarab; Valerii Matveev

doi:10.4028/www.scientific.net/AMM.763.170

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 763A Meshless Semi-Analytical Method for Solving...

A Meshless Semi-Analytical Method for Solving Convection Problems in Complex-Shaped Closed Cavities

Abstract:

Recently, a number of meshless techniques were proposed for solving convection-diffusion problems in arbitrarily shaped cavities. Unfortunately, most of them, including the finite difference or finite element methods, do not allow one to get a solution exactly satisfying boundary conditions for domains of irregular geometry. In this report a novel approach is proposed, which gives the possibility to avoid the necessity of constructing a complicated mesh in the neighborhood of the domain boundary. The technique is based on the R-function method combining the means of analytical geometry and projection techniques of mathematical physics, in particular the Galerkin method. Analytical expressions in the form of expansions in certain bases are obtained for the temperature, vorticity, and stream functions. Unlike other mesh and meshless techniques, these semi-analytical expressions satisfy boundary conditions exactly and approximate the temperature and velocity fields inside the cavity with accuracy depending on the number of terms of the expansion.

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Periodical:

Applied Mechanics and Materials (Volume 763)

Pages:

170-174

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.763.170

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Online since:

May 2015

Authors:

Mikhail Basarab*, Valerii Matveev

Keywords:

Closed Cavity, Natural Convection, RFM, R-Functions Method

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