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Journal of Scientific Computing

Erschienen in:

11.02.2016

An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids

verfasst von: Li Chen, Ruo Li

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2016

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Abstract

Linear reconstruction based on local cell-averaged values is the most commonly adopted technique to achieve a second-order accuracy when one uses the finite volume scheme on unstructured grids. For solutions with discontinuities appearing in such as conservation laws, a certain limiter has to be applied to the predicted gradient to prevent numerical oscillations. We propose in this paper a new formulation for linear reconstruction on unstructured grids, which integrates the prediction of the gradient and the limiter together. By solving on each cell a tiny linear programming problem without any parameters, the gradient is directly obtained which satisfies the monotonicity condition. It can be shown that the resulting numerical scheme with our new method fulfils a discrete maximum principle with fair relaxed geometric constraints on grids. Numerical results demonstrate that our method achieves satisfactory numerical accuracy with theoretical guarantee of local discrete maximum principle.

Vorheriger Artikel Discretization of div–curl Systems by Weak Galerkin Finite Element Methods on Polyhedral Partitions

Nächster Artikel Erratum to: An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids

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van Leer, B.: Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32(1), 101–136 (1979)CrossRef

Goodman, J.B., LeVeque, R.J.: On the accuracy of stable schemes for 2d scalar conversation laws. Math. Comput. 45(171), 15–21 (1985)MathSciNetMATH

Spekreijse, S.: Multigrid solution of monotone second-order discretizations of hyperbolic conservation laws. Math. Comput. 49(179), 135–155 (1987)MathSciNetCrossRefMATH

Barth, T.J., Jespersen, D.C.: The design and application of upwind schemes on unstructured meshes. In: 27th AIAA Aerospace Sciences Meeting, vol. 366, Jan 1989

Durlofsky, L.J., Engquist, B., Osher, S.: Triangle based adaptive stencils for the solution of hyperbolic conservation laws. J. Comput. Phys. 98(1), 64–73 (1992)CrossRefMATH

Batten, P., Lambert, C., Causon, D.M.: Positively conservative high-resolution convection schemes for unstructured elements. Int. J. Numer. Methods Eng. 39(11), 1821–1838 (1996)MathSciNetCrossRefMATH

Liu, X.D.: A maximum principle satisfying modification of triangle based adapative stencils for the solution of scalar hyperbolic conservation laws. SIAM J. Numer. Anal. 30(3), 701–716 (1993)MathSciNetCrossRefMATH

Hubbard, M.E.: Multidimensional slope limiters for MUSCL-type finite volume schemes on unstructured grids. J. Comput. Phys. 155(1), 54–74 (1999)MathSciNetCrossRefMATH

Park, J.S., Yoon, S.H., Kim, C.: Multi-dimensional limiting process for hyperbolic conservation laws on unstructured grids. J. Comput. Phys. 229(3), 788–812 (2010)MathSciNetCrossRefMATH

10.

Barth, T.J., Frederickson, P.O.: Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction. In: 28th AIAA Aerospace Sciences Meeting, vol. 13, Jan 1990

11.

Abgrall, R.: On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation. J. Comput. Phys. 114(1), 45–58 (1994)MathSciNetCrossRefMATH

12.

Friedrich, O.: Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids. J. Comput. Phys. 144(1), 194–212 (1998)MathSciNetCrossRef

13.

Hu, C., Shu, C.W.: Weighted essentially non-oscillatory schemes on triangular meshes. J. Comput. Phys. 150(1), 97–127 (1999)MathSciNetCrossRefMATH

14.

Liu, Y., Zhang, Y.T.: A robust reconstruction for unstructured WENO schemes. J. Sci. Comput. 54(2–3), 603–621 (2013)MathSciNetCrossRefMATH

15.

Jawahar, P., Kamath, H.: A high-resolution procedure for Euler and Navier–Stokes computations on unstructured grids. J. Comput. Phys. 164(1), 165–203 (2000)MathSciNetCrossRefMATH

16.

Li, W., Ren, Y.X., Lei, G., Luo, H.: The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids. J. Comput. Phys. 230(21), 7775–7795 (2011)MathSciNetCrossRefMATH

17.

Berger, M., Aftosmis, M.J., Murman, S.M.: Analysis of slope limiters on irregular grids. In: 43rd AIAA Aerospace Sciences Meeting, vol. 490, May 2005

18.

Buffard, T., Clain, S.: Monoslope and multislope MUSCL methods for unstructured meshes. J. Comput. Phys. 229(10), 3745–3776 (2010)MathSciNetCrossRefMATH

19.

May, S., Berger, M.: Two-dimensional slope limiters for finite volume schemes on non-coordinate-aligned meshes. SIAM J. Sci. Comput. 35(5), A2163–A2187 (2013)MathSciNetCrossRefMATH

20.

Shu, C.W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77(2), 439–471 (1988)MathSciNetCrossRefMATH

21.

Barth, T.J., Ohlberger, M.: Finite volume methods: foundation and analysis. In: Encyclopedia of Computational Mechanics. Citeseer, (2004)

22.

LeVeque, R.J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33(2), 627–665 (1996)MathSciNetCrossRefMATH

23.

Woodward, P., Colella, P.: The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54(1), 115–173 (1984)MathSciNetCrossRefMATH

Titel: An Integrated Linear Reconstruction for Finite Volume Scheme on Unstructured Grids
verfasst von: Li Chen
Ruo Li
Publikationsdatum: 11.02.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0173-1

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