Compact Third-Order Multidimensional Upwind Scheme for Navier-Stokes Simulations

• Published in: Theoretical and computational fluid dynamics Vol. 15; no. 6; pp. 373 - 401
• Main Authors: Caraeni, D., Fuchs, L.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01.07.2002
• Subjects: Algorithms; channel flow; Engineering and Technology; Finite element analysis; Fluid dynamics; Fluid Mechanics; Maskinteknik; Mechanical Engineering; Simulation; Strömningsmekanik; Teknik; Viscous flow
• ISSN: 0935-4964; 1432-2250; 1432-2250
• DOI: 10.1007/s00162-002-0060-2

A new compact third-order scheme for the solution of the unsteady Navier-Stokes equations on unstructured grids is proposed. The scheme is a cell-based algorithm, belonging to the class of Multidimensional Upwind schemes, which uses a finite-element reconstruction procedure over the cell to achieve third order (spatial) accuracy. Derivation of the scheme is given. The asymptotic accuracy, for steady/unsteady inviscid or viscous flow situations, is proved using numerical experiments. These results are compared with the performances of a second-order multidimensional upwind scheme. The new compact high-order discretization proves to have excellent parallel scalability, which makes it well suited for large-scale computations on parallel supercomputers. Our studies show clearly the advantages of the new compact third-order scheme compared with the classical second-order Multidimensional Upwind scheme. [PUBLICATION ABSTRACT]