Two dimensional solution of the advection-diffusion equation using two collocation methods with local upwinding RBF
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Inclou dades d'ús des de 2022
Cita com:
hdl:2117/192860
Tipus de documentText en actes de congrés
Data publicació2013
EditorCIMNE
Condicions d'accésAccés obert
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Abstract
The two-dimensional advection-diffusion equation is solved using two local
collocation methods with Multiquadric (MQ)Radial Basis Functions (RBFs). Although
both methods use upwinding, the first one, similar to the method of Kansa, approximates
the dependent variable with a linear combination of MQs. The nodes are grouped into
two types of stencil: cross-shaped stencil to approximate the Laplacian of the variable
and circular sector shape stencil to approximate the gradient components. The circular
sector opens in opposite to the flow direction and therefore the maximum number of nodes
and the shape parameter value are selected conveniently. The second method is based
on the Hermitian interpolation where the approximation function is a linear combination
of MQs and the resulting functions of applying partial differential equation (PDE) and
boundary operators to MQs, all of them centred at different points. The performance
of these methods is analysed by solving several test problems whose analytical solutions
are known. Solutions are obtained for different Peclet numbers, Pe, and several values
of the shape parameter. For high Peclet numbers the accuracy of the second method
is affected by the ill-conditioning of the interpolation matrix while the first interpolation method requires the introduction of additional nodes in the cross stencil. For low Pe both
methods yield accurate results. Moreover, the first method is employed to solve the twodimensional
Navier-Stokes equations in velocity-vorticity formulation for the lid-driven
cavity problem moderate Pe.
ISBN978-84-941407-6-1
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Coupled-2013-130_Two dimensional solution.pdf | 476,7Kb | Visualitza/Obre |