Abstract.
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.
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Received 29 October 2001 and accepted 21 March 2002
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Caraeni, D., Fuchs, L. Compact Third-Order Multidimensional Upwind Scheme for Navier–Stokes Simulations. Theoret Comput Fluid Dynamics 15, 373–401 (2002). https://doi.org/10.1007/s00162-002-0060-2
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DOI: https://doi.org/10.1007/s00162-002-0060-2