Radial Basis Function Based Partition of Unity Method for Two-Dimensional Unsteady Convection Diffusion Equations

G Krishna Veni; Chirala Satyanarayana; M Chenna Krishnareddy

doi:10.17485/IJST/v16i27.336

Article

Radial Basis Function Based Partition of Unity Method for Two-Dimensional Unsteady Convection Diffusion Equations

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i27.336

Year: 2023, Volume: 16, Issue: 27, Pages: 2090-2101

Original Article

Radial Basis Function Based Partition of Unity Method for Two-Dimensional Unsteady Convection Diffusion Equations

G Krishna Veni^1*, Chirala Satyanarayana², M Chenna Krishnareddy¹

¹Department of Mathematics, Osmania University College for Women, Hyderabad
²Department of Mathematics, Ecole Centrale School of Engineering, Mahindra University, Hyderabad

*Corresponding Author
Email: [email protected]

Received Date:09 June 2023, Accepted Date:17 June 2023, Published Date:20 July 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: The present method aims to solve and investigate the efficiency, accuracy, and stability of the 2D unsteady Navier-Stokes equation in stream function vorticity formulation and Taylor’s vortex problem. Method: RBF partition of unity method (RBF-PUM) was implemented to solve the twodimensional Navier- Stokes equations in stream function vorticity formulation and Taylor’s vortex problem. Findings: RBF-PUM results show good agreement with the exact solutions. The numerical approach is found to be efficient and accurate while maintaining stability even for a Reynolds number as high as 1000. The global RBF method’s high computational cost can be overcome by using the RBF-PUM. Novelty and applications: The RBF-PU methodology is extended to solve the two-dimensional Navier- Stokes equations in stream function vorticity formulation and Taylor’s vortex problem, which were not discussed earlier in the literature. The adaptive spatial refinement within the partitions may be performed independently using the RBF-PUM. Then it may be extended to the more complex problems in CFD.

Keywords: Mesh Free Methods; RBF- PUM; Navier- Stokes Equations; Taylor’s Vortex Problem; CFD

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Copyright

© 2023 Veni et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)