Assessment of Localization Strategies in a Radial Basis Function Meshless Method to Solve Two-Dimensional Convection-Diffusion Problems

Julian Mauricio Granados, Gabriel Arturo Oquendo, Carlos Andres Bustamante, Whady Felipe Florez

Research output: Chapter in Book/Report/Conference proceedingConference and proceedingspeer-review

Abstract

Two-dimensional Poisson and convection-diffusion problems are solved by using three localization schemes implemented in the context of a Radial Basis Function (RBFs) collocation method. The first scheme uses the traditional RBF superpositions to approximate the problem variable in a defined stencil. The second scheme is the Partition of Unity strategy and it is used to obtain a representation of governing equations as a linear combination of RBFs local superpositions evaluated at neighbouring stencils. Weight functions are designed to capture the convection term effect on the solution. In the third scheme, an upwind strategy is included in the Partition of Unity scheme for solving the convection-diffusion problem by moving and deforming stencils based on velocity. For all schemes, stencils in the form of crosses, circles, and squares are considered, and Root mean square (RMS) is obtained as a function of shape parameter, nodal distribution size and stencil size. In the case of Poisson problems, the use of Partition of unity in circular configuration with no more than 37 nodes per stencil is recommended as far as a c suitable range is obtained for each nodal distribution employed to avoid ill-conditioning issues.

Original languageEnglish
Title of host publication6th International Conference on Numerical Modelling in Engineering, NME 2023
EditorsMagd Abdel Wahab
PublisherTrans Tech Publications Ltd
Pages17-26
Number of pages10
ISBN (Print)978-303573806-3, 1662-8969
DOIs
StatePublished - 2024
Event6th International Conference on Numerical Modelling in Engineering, NME 2023 - Ghent, Belgium
Duration: 29 Aug 202331 Aug 2023

Publication series

NameAdvances in Science and Technology
Volume144
ISSN (Print)1662-8969
ISSN (Electronic)1662-0356

Conference

Conference6th International Conference on Numerical Modelling in Engineering, NME 2023
Country/TerritoryBelgium
CityGhent
Period29/08/2331/08/23

Bibliographical note

Publisher Copyright:
© 2024 Trans Tech Publications Ltd, Switzerland.

Keywords

  • Collocation Methods
  • Convection-Diffusion Problems
  • Localization Strategies
  • Radial Basis Functions

Types Minciencias

  • Eventos científicos con componente de apropiación

Fingerprint

Dive into the research topics of 'Assessment of Localization Strategies in a Radial Basis Function Meshless Method to Solve Two-Dimensional Convection-Diffusion Problems'. Together they form a unique fingerprint.

Cite this