Moving Kriging reconstruction for high-order finite volume computation of compressible flows

Abstract

This paper describes the development of a high-order finite volume method for the solution of compress-ible viscous flows on unstructured meshes. The novelty of this approach is based on the use of moving Kriging shape functions for the computation of the derivatives in the numerical flux reconstruction step at the cell faces. For each cell, the successive derivatives of the flow variables are deduced from the interpolation function constructed from a compact stencil support for both Gaussian and quartic spline correlation models. A particular attention is paid for the study of the influence of the correlation parameter onto the accuracy of the numerical scheme. The effect of the size of the moving Kriging stencil is also investigated. Robustness and convergence properties are studied for various inviscid and viscous flows. Results reveal that the moving Kriging shape function can be considered as an interesting alternative for the development of high-order methodology for complex geometries.

A second-order face-centred finite volume method for elliptic problems

“…Cell-centred and vertex-centred second-order finite volume (FV) methods are still the predominant techniques used in commercial and industrial computational fluid dynamics (CFD) solvers due to their robustness, easy implementation and relatively low cost [2,14,15,17,19,33]. Both, cellcentred and vertex-centred, FV techniques require a reconstruction of the gradient of the solution to ensure second-order convergence of the unknown and first-order convergence of the fluxes [1,3,11,12]. The accuracy of the scheme is therefore dependent on the accuracy of the reconstruction technique, which in turns depends on the quality of the mesh.…”

Moving Kriging shape function modeling of vector TARMA models for modal identification of linear time-varying structural systems

“…where UA ℝ n contains the values at support points x i (1 ri rn), λ i is the weight which is a function of x, and the shape function matrix Φ x ð ÞA ℝ n is decomposed based on a regression representation plus local departures [42][43][44] …”

“…Moving Kriging shape function is constructed by Moving Kriging interpolation in the compact support domain, which already has been applied to the mesh-free finite element method [42,43]. Stemmed from the idea of constructing the shape functions, a MK shape function modeling method is proposed for modal identification of LTV structural systems based on VTARMA models.…”

High-order flux reconstruction method for the hyperbolic formulation of the incompressible Navier-Stokes equations on unstructured grids

“…Extensions of FVM to higher orders of accuracy are often achieved through reconstruction of the state variables at the cell faces based on values at neighboring cell centers [1,2]. Reconstruction strategies commonly include polynomial reconstruction [1,3], moving Least-Squares [4][5][6], the Moving Kriging(MK)method [7] and interpolation by means of Radial basis functions (RBF) [8,9].…”