Premium
A modified multilevel meshfree algorithm for steady convection‐diffusion problems
Author(s) -
Barik Nikunja Bihari,
Tatavarthi Venkata Satya Sekhar
Publication year - 2021
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.4967
Subject(s) - radial basis function , convergence (economics) , nonlinear system , mathematics , algorithm , meshfree methods , convection–diffusion equation , node (physics) , diffusion , matrix (chemical analysis) , mathematical optimization , central processing unit , computer science , finite element method , mathematical analysis , physics , artificial neural network , artificial intelligence , materials science , quantum mechanics , economics , composite material , thermodynamics , economic growth , operating system
In this work, a modified multilevel augmented local radial basis function (RBF‐FD) meshfree algorithm is developed. The primary goal is the level‐by‐level calculation and then level‐by‐level correction from coarsest level to finest level node points. Numerical experiments are presented to verify the accuracy and efficiency of our developed algorithms with 2D convection‐diffusion problem and coupled nonlinear equations. Numerical results are presented through the figures and tables to demonstrate accuracy, efficiency, and convergence of the method. The developed scheme saves 56 % of the CPU time for the 2D convection‐diffusion problem and at least 86 % of the CPU time for coupled nonlinear equations than the usual local RBF method available in the literature. The iteration matrix of the modified multilevel RBF‐FD method satisfies the necessary and sufficient condition for convergence.