A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh (Communications in Computational Physics, 2018)
High-order discretization techniques offer the potential to significantly reducethe computational costs necessary to obtain accurate predictions when comparedto lower-order methods. However, efficient and universally-applicable high-orderdiscretizations remain somewhat illusive, especially for more arbitrary unstructuredmeshes and for incompressible/low-speed flows. A novel, high-order, central essentiallynon-oscillatory (CENO), cell-centered, finite-volume scheme is proposed forthe solution of the conservation equations of viscous, incompressible flows on three-dimensionalunstructured meshes. Similar to finite element methods, coordinate transformationsare used to maintain the scheme's order of accuracy even when dealingwith arbitrarily-shaped cells having non-planar faces. The proposed scheme is appliedto the pseudo-compressibility formulation of the steady and unsteady Navier-Stokesequations and the resulting discretized equations are solved with a parallel implicitNewton-Krylov algorithm. For unsteady flows, a dual-time stepping approachis adopted and the resulting temporal derivatives are discretized using the family ofhigh-order backward difference formulas (BDF). The proposed finite-volume schemefor fully unstructured mesh is demonstrated to provide both fast and accurate solutionsfor steady and unsteady viscous flows.