Arbitrary high order central non-oscillatory schemes on mixed-element unstructured meshes

In this paper we develop a family of very high-order central (up to 6th-order) non-oscillatory schemes for mixed-element unstructured meshes. The are inherently compact in the sense that stencils employed as possible, and directional reduced size therefore simplifying their implementation. Their key ingredient is non-linear combination CWENO style similar Dumbser et al [1] polynomial arising from stencil with lower-order polynomials stencils. Therefore, smooth regions computational domain optimum order accuracy recovered, while sharp-gradients larger influence reconstructions suppress oscillations. It compactness increases chances at least one them lying region data, greatly enhances robustness compared classical WENO schemes. two variants developed CWENOZ schemes, it first time such very-high-order designed We explore linear weights each assess performance terms accuracy, cost through series stringent 2D 3D test problems. results obtained demonstrate improved offer, parameter paramount importance potential use industrial-scale engineering applications.