A High-Order Central ENO Finite-Volume Scheme for Three-Dimensional Low-Speed Viscous Flows on Unstructured Mesh. (2nd April 2015)

• Record Type: Journal Article
• Authors: Charest, Marc R. J.; Groth, Clinton P. T.; Gauthier, Pierre Q.
• Is Part Of: Communications in computational physics. Volume 17:Number 3(2015:Mar.)
• Page Start: 615
• Page End: 656
• Publication Date: 2015-04-02
• Subjects: 35Q30, -- 65Z05, -- 65M08, -- 65N08, -- 76M12, -- 76D05, -- 76G25; Numerical algorithms, -- computational fluid dynamics, -- high-order methods, -- incompressible flows; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.091013.281114a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: High-order discretization techniques offer the potential to significantly reduce the computational costs necessary to obtain accurate predictions when compared to lower-order methods. However, efficient and universally-applicable high-order discretizations remain somewhat illusive, especially for more arbitrary unstructured meshes and for incompressible/low-speed flows. A novel, high-order, central essentially non-oscillatory (CENO), cell-centered, finite-volume scheme is proposed for the solution of the conservation equations of viscous, incompressible flows on three-dimensional unstructured meshes. Similar to finite element methods, coordinate transformations are used to maintain the scheme's order of accuracy even when dealing with arbitrarily-shaped cells having non-planar faces. The proposed scheme is applied to the pseudo-compressibility formulation of the steady and unsteady Navier-Stokes equations and the resulting discretized equations are solved with a parallel implicit Newton-Krylov algorithm. For unsteady flows, a dual-time stepping approach is adopted and the resulting temporal derivatives are discretized using the family of high-order backward difference formulas (BDF). The proposed finite-volume scheme for fully unstructured mesh is demonstrated to provide both fast and accurate solutions for steady and unsteady viscous flows.