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Quasi-ENO schemes for unstructured meshes based on umlimited data-dependent least-squares reconstruction. (English) Zbl 0899.76282
The paper concerns with high-order reconstruction of functions from cell-averaged values as a part of ENO-type methods. The least-square approach is used for fixed stencils with data-dependent weights. As a result, the author obtains a set of derivatives in the Taylor expansion series needed for the reconstruction. One of the main feature of the technique is its direct applicability to multidimensional unstructured meshes. Numerical examples for third- and fourth-order methods applied to smooth function reconstruction and the Euler equations are presented. In the latter case, unstructured meshes were used to calculate transonic airfoil flow.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
Software:
ANSLib
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References:
[1] T. J. Barth, P. O. Frederickson, Jan. 1990, AIAA Paper 90-0013
[2] V. Venkatakrishnan, Jan. 1993, AIAA Paper 93-0880
[3] Harten, A.; Osher, S., Uniformly high-order accurate nonoscillatory schemes, SIAM J. numer. anal., 24, 279, (1987) · Zbl 0627.65102
[4] Harten, A.; Osher, S.; Engquist, B.; Chakravarthy, S.R., Some results on uniformly high-order accurate essentially non-oscillatory schemes, Appl. numer. math., 2, 347, (1986) · Zbl 0627.65101
[5] Harten, A.; Engquist, B.; Osher, S.; Chakravarthy, S.R., Uniformly high order accurate essentially non-oscillatory schemes, III, J. comput. phys., 71, 231, (1987) · Zbl 0652.65067
[6] Liu, X.-D.; Osher, S.; Chan, T., Weighted essentially non-oscillatory schemes, J. comput. phys., 115, 200, (1994) · Zbl 0811.65076
[7] Jiang, G.-S.; Shu, C.-W., Efficient implementation of weighted ENO schemes, J. comput. phys., 126, 202, (1996) · Zbl 0877.65065
[8] Durlofsky, L.J.; Enquist, B.; Osher, S., Triangle based adaptive stencils for the solution of hyperbolic conservation laws, J. comput. phys., 98, 64, (1992) · Zbl 0747.65072
[9] Abgrall, R., On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation, J. comput. phys., 114, 45, (1994) · Zbl 0822.65062
[10] T. J. Barth, Jan. 1993, AIAA Paper 93-0668
[11] Golub, G.H.; van Loan, C.F., Matrix computations, (1983), Johns Hopkins Univ. Press Baltimore · Zbl 0559.65011
[12] Ollivier-Gooch, C.F., Multigrid acceleration of an upwind Euler solver on unstructured meshes, Aiaa j., 33, 1822, (1995) · Zbl 0856.76064
[13] C. F. Ollivier-Gooch, 1995, Towards Problem-Independent Multigrid Convergence Rates for Unstructured Mesh Methods I: Inviscid and Laminar Viscous Flows, Proceedings, Sixth International Symposium on Computational Fluid Dynamics, Japan Society of Computational Fluid Dynamics, University of California at Davis, Sept. 1995
[14] AGARD Fluid Dynamics Panel, May 1985, Test Cases for Inviscid Flow Field Methods, AGARD
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