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2013 | 11 | 8 | 1478-1488
Tytuł artykułu

A parameter-free smoothness indicator for high-resolution finite element schemes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite elements. The discrete maximum principle is enforced using a linearized flux-corrected transport algorithm. The deactivation of the flux limiter in regions of high regularity makes it possible to avoid the peak clipping effect at smooth extrema without generating spurious undershoots or overshoots elsewhere.
Wydawca
Czasopismo
Rocznik
Tom
11
Numer
8
Strony
1478-1488
Opis fizyczny
Daty
wydano
2013-08-01
online
2013-05-22
Twórcy
Bibliografia
  • [1] Cockburn B., Shu C.-W., The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems, J. Comput. Phys., 1998, 141(2), 199–224 http://dx.doi.org/10.1006/jcph.1998.5892
  • [2] Dolejší V., Feistauer M., On the discontinuous Galerkin method for the numerical solution of compressible high-speed flow, In: Numerical Mathematics and Advanced Applications, Ischia, July, 2001, Springer, Milan, 2003, 65–83
  • [3] John V., Schmeyer E., On finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion, Comput. Methods Appl. Mech. Engrg., 2008, 198(3–4), 475–494 http://dx.doi.org/10.1016/j.cma.2008.08.016
  • [4] Krivodonova L., Xin J., Remacle J.-F., Chevaugeon N., Flaherty J.E., Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, In: Workshop on Innovative Time Integrators for PDEs, Appl. Numer. Math., 2004, 48(3–4), 323–338 http://dx.doi.org/10.1016/j.apnum.2003.11.002
  • [5] Kuzmin D., Explicit and implicit FEM-FCT algorithms with flux linearization, J. Comput. Phys., 2009, 228(7), 2517–2534 http://dx.doi.org/10.1016/j.jcp.2008.12.011
  • [6] Kuzmin D., A vertex-based hierarchical slope limiter for p-adaptive discontinuous Galerkin methods, J. Comput. Appl. Math., 2010, 233(12), 3077–3085 http://dx.doi.org/10.1016/j.cam.2009.05.028
  • [7] Kuzmin D., Slope limiting for discontinuous Galerkin approximations with a possibly non-orthogonal Taylor basis, Internat. J. Numer. Methods Fluids, 2013, 71(9), 1178–1190 http://dx.doi.org/10.1002/fld.3707
  • [8] Kuzmin D., Möller M., Algebraic flux correction I. Scalar conservation laws, In: Flux-Corrected Transport, Sci. Comput., Springer, Berlin, 2005, 155–206 http://dx.doi.org/10.1007/3-540-27206-2_6
  • [9] Kuzmin D., Turek S., Flux correction tools for finite elements, J. Comput. Phys., 2002, 175(2), 525–558 http://dx.doi.org/10.1006/jcph.2001.6955
  • [10] LeVeque R.J., High-resolution conservative algorithms for advection in incompressible flow, SIAM J. Numer. Anal., 1996, 33(2), 627–665 http://dx.doi.org/10.1137/0733033
  • [11] Michoski C., Mirabito C., Dawson C., Wirasaet D., Kubatko E.J., Westerink J.J., Adaptive hierarchic transformations for dynamically p-enriched slope-limiting over discontinuous Galerkin systems of generalized equations, J. Comput. Phys., 2010, 230(22), 8028–8056 http://dx.doi.org/10.1016/j.jcp.2011.07.009
  • [12] Persson P.-O., Peraire J., Sub-cell shock capturing for discontinuous Galerkin methods, In: 44th AIAA Aerospace Sciences Meeting, Reno, January, 2006, preprint available at http://acdl.mit.edu/peraire/PerssonPeraire_ShockCapturing.pdf
  • [13] Qiu J., Shu C.-W., A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin methods using weighted essentially nonoscillatory limiters, SIAM J. Sci. Comput. 2005, 27(3), 995–1013 http://dx.doi.org/10.1137/04061372X
  • [14] Schieweck F., A general transfer operator for arbitrary finite element spaces, Preprint 25/00, Otto-von-Guericke Universität Magdeburg, 2000
  • [15] Schieweck F., Skrzypacz P., A local projection stabilization method with shock capturing and diagonal mass matrix for solving non-stationary transport dominated problems, Comput. Methods Appl. Math., 2012, 12(2), 221–240
  • [16] Yang M., Wang Z.J., A parameter-free generalized moment limiter for high-order methods on unstructured grids, Adv. Appl. Math. Mech., 2009, 1(4), 451–480
  • [17] Zalesak S.T., Fully multidimensional flux-corrected transport algorithms for fluids, J. Comput. Phys., 1979, 31(3), 335–362 http://dx.doi.org/10.1016/0021-9991(79)90051-2
  • [18] Zienkiewicz O.C., Zhu J.Z., A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. Numer. Methods Engrg., 1987, 24(2), 337–357 http://dx.doi.org/10.1002/nme.1620240206
  • [19] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Internat. J. Numer. Methods Engrg., 1992, 33(7), 1331–1364 http://dx.doi.org/10.1002/nme.1620330702
  • [20] Zienkiewicz O.C., Zhu J.Z., The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, Internat. J. Numer. Methods Engrg., 1992, 33(7), 1365–1382 http://dx.doi.org/10.1002/nme.1620330703
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-013-0254-4
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