A modified multilevel meshfree algorithm for Steady Convection‐Diffusion Problems

2021 ◽  
Author(s):  
Nikunja Bihari Barik ◽  
T. V. S. Sekhar
Keyword(s):  
Convection Diffusion ◽  
Steady Convection ◽  
Diffusion Problems

An Efficient Local RBF Meshless Scheme for Steady Convection–Diffusion Problems

2017 ◽  
Vol 14 (06) ◽  
pp. 1750064 ◽  
Author(s):  
Nikunja Bihari Barik ◽  
T. V. S. Sekhar
Keyword(s):  
Shape Parameter ◽  
Stable Solution ◽  
Navier Stokes ◽  
Computational Time ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Cpu Time ◽  
Numerical Studies ◽  
Steady Convection ◽  
Diffusion Problems

The efficiency of any numerical scheme measures on the accuracy of the scheme and its computational time. In this work, an efficient augmented local radial basis function finite difference (RBF-FD) scheme has been developed for steady convection–diffusion problems. The accommodative full approximation scheme–full multigrid (FAS-FMG) analogy with local refinement is adopted to achieve this efficiency. The efficiency of the method is illustrated through linear convection–diffusion equation, coupled nonlinear equation and for the incompressible Navier–Stokes (NS) equations. Numerical studies are made by using multiquadric (MQ) RBF. The upwind type nodes are considered to handle convective terms effectively for NS equations. The developed scheme saves 70–80% of the CPU time for the first two model problems and at least 50% of the CPU time for NS equations than the usual RBF-FD method found in the literature. It is found that there are optimum sets of nodes which give accurate and stable solution. It is also found that the value of the shape parameter will be lower when the number of nodes is higher. But higher the value of Re, higher will be the shape parameter.

A Wavelet-Based Adaptive Finite Element Method for Advection-Diffusion Equations

1997 ◽  
Vol 07 (02) ◽  
pp. 265-289 ◽  
Author(s):  
C. Canuto ◽  
I. Cravero
Keyword(s):  
Finite Element ◽  
Unstructured Mesh ◽  
Adaptive Finite Element Method ◽  
Adaptive Finite Element ◽  
Element Mesh ◽  
Convection Diffusion ◽  
Grid Points ◽  
Convection Dominated ◽  
Steady Convection ◽  
Diffusion Problems

We propose a wavelet-based procedure for adapting a finite element mesh to the structure of the solution. After a finite element solution is computed on a given unstructured mesh, it is wavelet-analyzed on a superimposed regular dyadic grid; the analysis leads to an adapted distribution of grid points, which defines the new unstructured mesh via a Delaunay triangulation. Several examples of discretizations of steady convection-diffusion problems in the convection-dominated regime indicate the feasibility of our approach.

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