Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2018

07.10.2017

Higher Order Finite Volume Central Schemes for Multi-dimensional Hyperbolic Problems

verfasst von: Prabal Singh Verma, Wolf-Christian Müller

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order accurate finite volume central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and shock capturing nature of the scheme are demonstrated in various nonlinear multi-dimensional problems. In order to show the overall performance of the present central scheme numerical errors and non-oscillatory behavior are compared with existing multi-dimensional CWENO based central schemes for various multi-dimensional problems. Moreover, the benefits of the present fourth order central scheme over third order implementation are shown by comparing the numerical dissipation and computational cost between the two.
Vorheriger Artikel A Dual Consistent Finite Difference Method with Narrow Stencil Second Derivative Operators
Nächster Artikel A Fractional Order Collocation Method for Second Kind Volterra Integral Equations with Weakly Singular Kernels

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Balbás, J., Tadmor, E.: Nonoscillatory central schemes for one-and two-dimensional magnetohydrodynamics equations. II: High-order semidiscrete schemes. SIAM J. Sci. Comput. 28(2), 533–560 (2006)MathSciNetMATHCrossRef
2.
Bianco, F., Puppo, G., Russo, G.: High-order central schemes for hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 21(1), 294–322 (1999)MathSciNetMATHCrossRef
3.
Bryson, S., Levy, D.: High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton–Jacobi equations. J. Comput. Phys. 189(1), 63–87 (2003)MathSciNetMATHCrossRef
4.
Buchmüller, P., Helzel, C.: Improved accuracy of high-order WENO finite volume methods on cartesian grids. J. Sci. Comput. 61(2), 343–368 (2014)MathSciNetMATHCrossRef
5.
Cai, L., Feng, J.-H., Xie, W.-X.: A CWENO-type central-upwind scheme for ideal MHD equations. Appl. Math. Comput. 168(1), 600–612 (2005)MathSciNetMATH
6.
Capdeville, G.: A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes. J. Comput. Phys. 227(5), 2977–3014 (2008)MathSciNetMATHCrossRef
7.
Capdeville, G.: A high-order multi-dimensional HLL-Riemann solver for non-linear euler equations. J. Comput. Phys. 230(8), 2915–2951 (2011)MathSciNetMATHCrossRef
8.
Castro, C.E., Toro, E.F.: Solvers for the high-order Riemann problem for hyperbolic balance laws. J. Comput. Phys. 227(4), 2481–2513 (2008)MathSciNetMATHCrossRef
9.
Cravero, I., Semplice, M.: On the accuracy of WENO and CWENO reconstructions of third order on nonuniform meshes. J. Sci. Comput. 67(3), 1219–1246 (2016)MathSciNetMATHCrossRef
10.
Friedrichs, K.O., Lax, P.D.: Systems of conservation equations with a convex extension. Proc. Nat. Acad. Sci. 68(8), 1686–1688 (1971)MathSciNetMATHCrossRef
11.
Godunov, S.K.: A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Matematicheskii Sbornik 89(3), 271–306 (1959)MathSciNetMATH
12.
Holden, H., Lie, K.-A., Risebro, N.H.: An unconditionally stable method for the Euler equations. J. Comput. Phys. 150(1), 76–96 (1999)MathSciNetMATHCrossRef
13.
Hu, C., Shu, C.-W.: Weighted essentially non-oscillatory schemes on triangular meshes. J. Comput. Phys. 150(1), 97–127 (1999)MathSciNetMATHCrossRef
14.
Hu, X.Y., Wang, Q., Adams, N.A.: An adaptive central-upwind weighted essentially non-oscillatory scheme. J. Comput. Phys. 229(23), 8952–8965 (2010)MathSciNetMATHCrossRef
15.
Huang, C.-S., Arbogast, T., Hung, C.-H.: A re-averaged WENO reconstruction and a third order CWENO scheme for hyperbolic conservation laws. J. Comput. Phys. 262, 291–312 (2014)MathSciNetMATHCrossRef
16.
Ivan, L., Groth, C.P.T.: High-order solution-adaptive central essentially non-oscillatory (ceno) method for viscous flows. J. Comput. Phys. 257, 830–862 (2014)MathSciNetMATHCrossRef
17.
Ivan, L., De Sterck, H., Susanto, A., Groth, C.P.T.: High-order central eno finite-volume scheme for hyperbolic conservation laws on three-dimensional cubed-sphere grids. J. Comput. Phys. 282, 157–182 (2015)MathSciNetMATHCrossRef
18.
Ketcheson, D.I.: Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations. SIAM J. Sci. Comput. 30(4), 2113–2136 (2008)MathSciNetMATHCrossRef
19.
Kissmann, R., Grauer, R.: A low dissipation essentially non-oscillatory central scheme. Comput. Phys. Commun. 176(8), 522–530 (2007)MathSciNetMATHCrossRef
20.
Kleimann, J., Kopp, A., Fichtner, H., Grauer, R., Germaschewski, K.: Three-dimensional MHD high-resolution computations with CWENO employing adaptive mesh refinement. Comput. Phys. Commun. 158(1), 47–56 (2004)MATHCrossRef
21.
Kurganov, A., Levy, D.: A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations. SIAM J. Sci. Comput. 22(4), 1461–1488 (2000)MathSciNetMATHCrossRef
22.
Kurganov, A., Levy, D.: Central-upwind schemes for the saint-venant system. ESAIM Math. Model. Numer. Anal. 36(3), 397–425 (2002)MathSciNetMATHCrossRef
23.
Kurganov, A., Petrova, G.: A third-order semi-discrete genuinely multidimensional central scheme for hyperbolic conservation laws and related problems. Numer. Math. 88(4), 683–729 (2001)MathSciNetMATHCrossRef
24.
Kurganov, A., Tadmor, E.: New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160(1), 241–282 (2000)MathSciNetMATHCrossRef
25.
Kurganov, A., Tadmor, E.: Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Numer. Methods Partial Differ. Equ. 18(5), 584–608 (2002)MathSciNetMATHCrossRef
26.
Kurganov, A., Noelle, S., Petrova, G.: Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations. SIAM J. Sci. Comput. 23(3), 707–740 (2001)MathSciNetMATHCrossRef
27.
Lahooti, M., Pishevar, A.: A new fourth order central WENO method for 3d hyperbolic conservation laws. Appl. Math. Comput. 218(20), 10258–10270 (2012)MathSciNetMATH
28.
Langseth, J.O., LeVeque, R.J.: A wave propagation method for three-dimensional hyperbolic conservation laws. J. Comput. Phys. 165(1), 126–166 (2000)MathSciNetMATHCrossRef
29.
Levy, D.: Third-order 2D Central Schemes for Conservation Laws, vol. I, pp. 489–504. INRIA School on Hyperbolic Systems (1998)
30.
Levy, D., Puppo, G., Russo, G.: Central weno schemes for hyperbolic systems of conservation laws. ESAIM Math. Model. Numer. Anal. 33(3), 547–571 (1999)MathSciNetMATHCrossRef
31.
Levy, D., Puppo, G., Russo, G.: A third order central weno scheme for 2d conservation laws. Appl. Numer. Math. 33(1–4), 415–421 (2000)MathSciNetMATHCrossRef
32.
Levy, D., Puppo, G., Russo, G.: Compact central weno schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22(2), 656–672 (2000)MathSciNetMATHCrossRef
33.
Levy, D., Puppo, G., Russo, G.: On the behavior of the total variation in cweno methods for conservation laws. Appl. Numer. Math. 33(1–4), 407–414 (2000)MathSciNetMATHCrossRef
34.
Levy, D., Puppo, G., Russo, G.: A fourth-order central weno scheme for multidimensional hyperbolic systems of conservation laws. SIAM J. Sci. Comput. 24(2), 480–506 (2002)MathSciNetMATHCrossRef
35.
McCorquodale, P., Colella, P.: A high-order finite-volume method for conservation laws on locally refined grids. Commun. Appl. Math. Comput. Sci. 6(1), 1–25 (2011)MathSciNetMATHCrossRef
36.
Nessyahu, H., Tadmor, E.: Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87(2), 408–463 (1990)MathSciNetMATHCrossRef
37.
Núñez-De La Rosa, J., Munz, C.-D.: xtroem-fv: a new code for computational astrophysics based on very high order finite-volume methods-I. Magnetohydrodynamics. Mon. Not. R. Astron. Soc. 455(4), 3458–3479 (2016)CrossRef
38.
Price, D.J.: Modelling discontinuities and Kelvin–Helmholtz instabilities in sph. J. Comput. Phys. 227(24), 10040–10057 (2008)MathSciNetMATHCrossRef
39.
Qiu, J., Shu, C.-W.: On the construction, comparison, and local characteristic decomposition for high-order central weno schemes. J. Comput. Phys. 183(1), 187–209 (2002)MathSciNetMATHCrossRef
40.
Schulz-Rinne, C.W., Collins, J.P., Glaz, H.M.: Numerical solution of the Riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput. 14(6), 1394–1414 (1993)MathSciNetMATHCrossRef
41.
Semplice, M., Coco, A., Russo, G.: Adaptive mesh refinement for hyperbolic systems based on third-order compact weno reconstruction. J. Sci. Comput. 66(2), 692–724 (2016)MathSciNetMATHCrossRef
42.
Shi, J., Changqing, H., Shu, C.-W.: A technique of treating negative weights in weno schemes. J. Comput. Phys. 175(1), 108–127 (2002)MATHCrossRef
43.
Shu, C.-W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Quarteroni, A.M. (ed.) Advanced Numerical Approximation of Nonlinear Hyperbolic Equations, pp. 325–432. Springer, Berlin (1998)CrossRef
44.
Shu, C.-W.: High order weighted essentially nonoscillatory schemes for convection dominated problems. SIAM Rev. 51(1), 82–126 (2009)MathSciNetMATHCrossRef
45.
Sod, G.A.: A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comput. Phys. 27(1), 1–31 (1978)MathSciNetMATHCrossRef
46.
Titarev, V.A., Toro, E.F.: Finite-volume weno schemes for three-dimensional conservation laws. J. Comput. Phys. 201(1), 238–260 (2004)MathSciNetMATHCrossRef
47.
Tokareva, S.A., Toro, E.F.: HLLC-type Riemann solver for the Baer–Nunziato equations of compressible two-phase flow. J. Comput. Phys. 229(10), 3573–3604 (2010)MathSciNetMATHCrossRef
48.
Toro, E.F.: Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. Springer, Berlin (2013)
49.
Metadaten
Titel
Higher Order Finite Volume Central Schemes for Multi-dimensional Hyperbolic Problems
verfasst von
Prabal Singh Verma
Wolf-Christian Müller
Publikationsdatum
07.10.2017
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2018
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-017-0567-8

Weitere Artikel der Ausgabe 2/2018

Journal of Scientific Computing 2/2018 Zur Ausgabe

OriginalPaper

Generalized Deconvolution Procedure for Structural Modeling of Turbulence

OriginalPaper

Hybrid Spectral Difference Methods for Elliptic Equations on Exterior Domains with the Discrete Radial Absorbing Boundary Condition

OriginalPaper

Flows Generating Nonlinear Eigenfunctions

OriginalPaper

A Fractional Order Collocation Method for Second Kind Volterra Integral Equations with Weakly Singular Kernels

OriginalPaper

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

OriginalPaper

Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold Model