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.