Radial basis function-generated finite differences solution of natural convection problem in 3D

2020 ◽  
Author(s):  
Gregor Kosec ◽  
Jure Slak
Keyword(s):  
Natural Convection ◽  
Radial Basis Function ◽  
Basis Function ◽  
Finite Differences ◽  
Radial Basis ◽  
Convection Problem ◽  
Natural Convection Problem

Seismic modeling with radial-basis-function-generated finite differences

Geophysics ◽  
2015 ◽  
Vol 80 (4) ◽  
pp. T137-T146 ◽  
Author(s):  
Bradley Martin ◽  
Bengt Fornberg ◽  
Amik St-Cyr
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Finite Differences ◽  
Seismic Modeling ◽  
Radial Basis

scholarly journals A Strong-Form Off-Lattice Boltzmann Method for Irregular Point Clouds

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1802
Author(s):  
Ivan Pribec ◽  
Thomas Becker ◽  
Ehsan Fattahi
Keyword(s):  
Radial Basis Function ◽  
Lattice Boltzmann Method ◽  
Basis Function ◽  
Lattice Boltzmann ◽  
Finite Differences ◽  
Strong Form ◽  
Lattice Boltzmann Methods ◽  
Radial Basis ◽  
Irregular Point ◽  
Boltzmann Method

Radial basis function generated finite differences (RBF-FD) represent the latest discretization approach for solving partial differential equations. Their benefits include high geometric flexibility, simple implementation, and opportunity for large-scale parallel computing. Compared to other meshfree methods, typically based upon moving least squares (MLS), the RBF-FD method is able to recover a high order of algebraic accuracy while remaining better conditioned. These features make RBF-FD a promising candidate for kinetic-based fluid simulations such as lattice Boltzmann methods (LB). Pursuant to this approach, we propose a characteristic-based off-lattice Boltzmann method (OLBM) using the strong form of the discrete Boltzmann equation and radial basis function generated finite differences (RBF-FD) for the approximation of spatial derivatives. Decoupling the discretizations of momentum and space enables the use of irregular point cloud, local refinement, and various symmetric velocity sets with higher order isotropy. The accuracy and computational efficiency of the proposed method are studied using the test cases of Taylor–Green vortex flow, lid-driven cavity, and periodic flow over a square array of cylinders. For scattered grids, we find the polyharmonic spline + poly RBF-FD method provides better accuracy compared to MLS. For Cartesian node layouts, the results are the opposite, with MLS offering better accuracy. Altogether, our results suggest that the RBF-FD paradigm can be applied successfully also for kinetic-based fluid simulation with lattice Boltzmann methods.

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