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

► A high-order finite volume method is developed for viscous flows on unstructured grid. ► The novelty of this approach is based on the use of moving Kriging shape functions. ► Gaussian and quartic spline correlations are considered for high-order reconstruction. ► The effect of the size of the reconstruction stencil is investigated. ► Accuracy and robustness are studied for both steady and unsteady problems. This paper describes the development of a high-order finite volume method for the solution of compressible 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.