High-Order CENO Finite-Volume Schemes for Multi-Block Unstructured Mesh

High-order discretization techniques remain an active area of research in Computational Fluid Dynamics (CFD) since they offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lowerorder methods. In spite of the successes to date, efficient, universally-applicable, highorder discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes. A novel, high-order, Central Essentially Non Oscillatory (CENO), cell-centered, finite-volume scheme is examined for the solution of the conservation equations of inviscid, compressible, gas dynamics on multi-block unstructured meshes. This scheme was implemented for both two- and three-dimensional meshes consisting of triangular and tetrahedral computational cells, respectively. The CENO scheme is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact, least-squares reconstruction technique with a monotonicity preserving limited piecewise linear least-squares reconstruction algorithm. Fixed central stencils are used for both the unlimited high-order k-exact reconstruction and the limited piecewise linear reconstruction. In the proposed hybrid procedure, switching between the two reconstruction algorithms is determined by a solution smoothness indicator that indicates whether or not the solution is resolved on the computational mesh. This hybrid approach avoids the complexities associated with reconstruction on multiple stencils that other essentially non-oscillatory (ENO) and weighted ENO schemes can encounter. As such, it is well suited for solution reconstruction on unstructured mesh. The CENO scheme for unstructured mesh is described and analyzed in terms of accuracy, computational cost, and parallel performance. In particular, the accuracy of reconstructed solutions for arbitrary functions and idealized flows is investigated as a function of mesh resolution. The ability of the scheme to accurately represent solutions with smooth extrema while maintaining robustness in regions of under-resolved and/or nonsmooth solution content (i.e., solutions with shocks and discontinuities) is demonstrated for a range of problems.

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