On The Accuracy Of Integral Representation Of
Differential Operators In Lagrangian Blob
Mesh-less Methods
Author(s)
C. Golia & B. Buonomo
Abstract
We explore novel ideas to improve the accuracy of the integral approximation of
differential operators (Gradient and Laplacian) in the simulation of thermal
viscous problems with Lagrangian Blob mesh-less methods.
Basically we investigate and develop a novel convolution integral
discretization of the differential operators by using 2D-Taylor series expansions
and a Gaussian like kernel function defined on a compact support around the
blob centre of a given particle.
This allows us to overtake:
• deficiency of cells in the compact domain due to irregular distribution of the
particles around the given blob,
• deficiency of cells in the compact domain caused by the presence of a
boundary cutting the support of a nearby blob.
The accuracy and order of approximation of such a discretization are determined
in regular and randomly distorted grids of various sizes, and compared with the
widely used PSE (Particle Strength Exchange) formulation.
Results obtained in the solution of thermal buoyant problems at realistic
values of the Grashoff number demonstrate validity and benefits of the novel
findings.
Keywords: integral definition of differential operators, lagrangian mesh-less
methods, vortex/thermal blobs, thermal buoyant problems.
Keywords
integral definition of differential operators, lagrangian mesh-less
methods, vortex/thermal blobs, thermal buoyant problems.
Related Book
Other papers in this volume
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