2022/01/05 by Robert J. Watson, Will Trojak, Watson, Rob +1
Engineering · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Magnetic confinement fusion research #Numerical Analysis (math.NA) #Particle accelerators and beam dynamics
paper · pdf · doi:10.48550/arxiv.2201.01548
openalex publication_date 2022/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions as a methods for underlying functional approximation is explored in one dimension, using both analytical and numerical methods. At some mesh densities, RBF flux reconstruction is found to outperform polynomial flux reconstruction, and this range of mesh densities becomes finer as the width of the RBF interpolator is increased. A method which avoids the poor conditioning of flat RBFs is used to test a wide range of basis shapes, and at very small values, the polynomial behaviour is recovered. Changing the location of the solution points is found to have an effect similar to that in polynomial FR, with the Gauss--Legendre points being the most effective. Altering the location of the functional centres is found to have only a very small effect on performance. Similar behaviours are determined for the non-linear Burgers' equation.