Numerical study of radial basis function interpolation for data transfer across discontinuous mesh interfaces

Abstract

SUMMARYAllowing discontinuous or non‐matching mesh spacing across zonal interfaces within a computational domain offers many advantages, particularly in terms of easing the mesh generation process, reduction of required mesh densities, and relative motion between mesh zones. This paper presents a numerical study of a universal method for interpolating solution data across such interfaces. The method utilises radial basis functions (RBFs) for n‐dimensional volume interpolation, and treats the available solution data points simply as arbitrary clouds of points, eliminating all connectivity requirements and making it applicable to a wide range of computational problems. Properties of the developed meshless interface interpolation are investigated using analytic functions, and three issues are considered: the achievable order of spatial accuracy of the RBF interpolation alone and comparison with a variable order polynomial; the effect of a combined RBF and polynomial interpolation; and the ability of the method to recover frequency content. RBF interpolation alone is shown to achieve fourth‐order to sixth‐order spatial accuracy in one and two dimensions, and in three dimensions, using a small number of data points, third‐order and above is achievable even for a 3 : 1 discontinuous cell spacing ratio, that is a 27 : 1 volume ratio, across the interface. Hence, it is inefficient to include polynomial terms, since improving on the RBF spatial accuracy results in a significant increase in the system size and deterioration in conditioning. It is also shown that only five points per wavelength are required to capture both frequency and amplitude content of periodic solutions to less than 0.01% error.Copyright © 2013 John Wiley & Sons, Ltd.

A technique of flux reconstruction at the interfaces of nonconforming grids for aeroacoustic simulations

“…These n v cells are located along the line i ′ =0 for a 2‐D mesh, in the plane i ′ =0 for a 3‐D straight mesh. The RBF approximation u RBF of the variable u at point x writes where ξ j and ζ q are the unknown interpolation coefficients, are the centers of the n v cells, Φ are Wendland's RBFs, and is a polynomial term of degree deg(P) that ensures the unicity of the approximation u RBF . The calculation of the coefficients ξ j and ζ q is presented in Appendix A.1.…”

“…To perform aeroacoustic simulations of high‐Reynolds‐number flows at a reasonable computational cost, the use of nonconforming grids without overlapping is attractive. Such meshes exhibit discontinuities of the grid lines across the block interface.…”

“…Due to the mesh line discontinuities at the grid interface, an additional step consisting in reconstructing ghost cells is required. The flow variables in the ghost cells are computed using a local interpolation technique, based on a meshless method involving radial basis functions (RBFs) . Meshless interpolations are useful in alleviating the difficulties caused by the loss of the mesh topology at the interfaces of nonconforming grids.…”

“…The flow variables in the ghost cells are computed using a local interpolation technique, based on a meshless method involving radial basis functions (RBFs). 9,18 Meshless interpolations are useful in alleviating the difficulties caused by the loss of the mesh topology at the interfaces of nonconforming grids. Indeed, since meshless interpolations are performed from arbitrarily scattered spatial data without any geometrical information, computational overheads due to topology reconstructions are avoided.…”

Enhancing performance and scalability of data transfer across sliding grid interfaces for time-accurate unsteady simulations of multistage turbomachinery flows

“…They enjoy various degrees of accuracy, optimality, efficiency and physical conservation properties [2,3,4]. However, as the modern applications grow in scale, the current algorithms run into some performance limitations.…”