@Article{CiCP-27-2,
author = {Monysekar, K. and Y., V., Sanyasiraju, S., S.},
title = {Upwind Biased Local RBF Scheme with PDE Centres for the Steady Convection Diffusion Equations with Continuous and Discontinuous Boundary Conditions},
journal = {Communications in Computational Physics},
year = {2020},
volume = {27},
number = {2},
pages = {460--479},
abstract = {<p style="text-align: justify;">RBF based grid-free scheme with PDE centres is experimented in this work
for solving Convection-Diffusion Equations (CDE), a simplified model of the Navier-Stokes equations. For convection dominated problems, very few integration schemes
can give converged solutions for the entire range of diffusivity wherein sharp layers are
expected in the solutions and accurate computation of these layers is a big challenge
for most of the numerical schemes. Radial Basis Function (RBF) based Local Hermitian
Interpolation (LHI) with PDE centres is one such integration scheme which has some
built in upwind effect and hence may be a good solver for the convection dominated
problems. In the present work, to get convergent solutions consistently for small diffusion parameters, an explicit upwinding is also introduced in to the RBF based scheme
with PDE centres, which was initially used to solve some time dependent problems
in [10]. RBF based numerical schemes are one type of grid free numerical schemes
based on the radial distances and hence very easy to use in high dimensional problems. In this work, the RBF scheme, with different upwind biasing, is used to a variety
of steady benchmark problems with continuous and discontinuous boundary data and
validated against the corresponding exact solutions. Comparisons of the solutions of
the convective dominant benchmark problems show that the upwind biasing either
in source centres or PDE centres gives convergent solutions consistently and is stable
without any oscillations especially for problems with discontinuities in the boundary
conditions. It is observed that the accuracy of the solutions is better than the solutions
of other standard integration schemes particularly when the computations are carried
out with fewer centers.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2018-0054},
url = {https://global-sci.com/article/79770/upwind-biased-local-rbf-scheme-with-pde-centres-for-the-steady-convection-diffusion-equations-with-continuous-and-discontinuous-boundary-conditions}
}