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 2/2020

01.02.2020

An \(h-\)Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model

verfasst von: Lulu Tian, Hui Guo, Rui Jia, Yang Yang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2020

Einloggen

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

search-config
loading …

Abstract

In this paper, we apply local discontinuous Galerkin methods to the compressible wormhole propagation. With high velocity, Darcy–Forchheimer model is used instead of classical Darcy framework. Optimal error estimates for the pressure, velocity, porosity and concentration in different norms are established on non-uniform rectanglular grids. To capture the propagation of the wormhole accurately and save computations, adaptive mesh is applied. Numerical experiments are presented to verify the theoretical analysis and show the good performance of the LDG scheme for compressible wormhole propagation.
Vorheriger Artikel High Order Still-Water and Moving-Water Equilibria Preserving Discontinuous Galerkin Methods for the Ripa Model
Nächster Artikel Nonoverlapping Localized Exponential Time Differencing Methods for Diffusion Problems

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.
Ainsworth, M., Oden, J.T.: A posteriori error estimation in finite element analysis. Comput. Methods Appl. Mech. Eng. 142, 1–88 (1997)MathSciNetMATH
2.
Bassi, F., Rebay, S.: A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier–Stokes equations. J. Comput. Phys. 131, 267–279 (1997)MathSciNetMATH
3.
Braack, M., Prohl, A.: Stable discretization of a diffuse interface model for liquid–vapor flows with surface tension. ESAIM Math. Model. Numer. Anal. 47, 401–420 (2013)MathSciNetMATH
4.
Berger, M.J., Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82, 64–84 (1989)MATH
5.
Castillo, P., Cockburn, B., Perugia, I., Schötzau, D.: Superconvergence of the local discontinuous Galerkin method for elliptic problems on Cartesian grids. SIAM J. Numer. Anal. 39, 264–285 (2001)MathSciNetMATH
6.
Chuenjarern, N., Xu, Z., Yang, Y.: High-order bound-preserving discontinuous Galerkin methods for compressible miscible displacements in porous media on triangular meshes. J. Comput. Phys. 378, 110–128 (2019)MathSciNetMATH
7.
Ciarlet, P.: The Finite Element Method for Elliptic Problem. SIAM, Philadelphia (1975)
8.
Cockburn, B., Hou, S., Shu, C.W.: The Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: the multidimensional case. Math. Comput. 54, 545–581 (1990)MathSciNetMATH
9.
Cockburn, B., Lin, S.Y., Shu, C.W.: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: one-dimensional systems. J. Comput. Phys. 84, 90–113 (1989)MathSciNetMATH
10.
Cockburn, B., Shu, C.W.: TVB Runge–Kutta local projection discontinuous Galerkin finite element method for conservation laws. II: general framework. Math. Comput. 52, 411–435 (1989)MathSciNetMATH
11.
Cockburn, B., Shu, C.W.: The Runge–Kutta discontinuous Galerkin method for conservation laws. V: multidimensional systems. J. Comput. Phys. 141, 199–224 (1998)MathSciNetMATH
12.
Cockburn, B., Shu, C.-W.: The local discontinuous Galerkin method for time-dependent convection–diffusion systems. SIAM J. Numer. Anal. 35, 2440–2463 (1998)MathSciNetMATH
13.
Diehl, D.: Higher Order Schemes for Simulation of Compressible Liquid–Vapor Flows with Phase Change. Universität Freiburg, Freiburg im Breisgau (2007)MATH
14.
Fredd, C.N., Fogler, H.S.: Influence of transport and reaction on wormhole formation in porous media. Fluid Mech. Transp. Phenom. 44, 1933–1949 (1998)
15.
Gelfand, I.M.: Some questions of analysis and differential equations. Am. Math. Soc. Transl 26, 201–219 (1963)MathSciNet
16.
Golfier, F., Zarcone, C., Bazin, B., Lenormand, R., Lasseux, D., Quintard, M.: On the ability of a Darcy-scale model to capture wormhole formation during the dissolution of a porous medium. J. Fluid Mech. 457, 213–254 (2002)MATH
17.
Guo, H., Tian, L., Xu, Z., Yang, Y., Qi, N.: High-order local discontinuous Galerkin method for simulating wormhole propagation. J. Comput. Appl. Math. 350, 247–261 (2019)MathSciNetMATH
18.
Guo, H., Yang, Y.: Bound-preserving discontinuous Galerkin method for compressible miscible displacement problem in porous media. SIAM J. Sci. Comput. 39, A1969–A1990 (2017)MATH
19.
Guo, H., Zhang, Q., Wang, J.: Error analysis of the semi-discrete local discontinuous Galerkin method for compressible miscible displacement problem in porous media. Appl. Math. Comput. 259, 88–105 (2015)MathSciNetMATH
20.
Guo, H., Yu, F., Yang, Y.: Local discontinuous Galerkin method for incompressible miscible displacement problem in porous media. J. Sci. Comput. 71, 615–633 (2017)MathSciNetMATH
21.
Hurd, A.E., Sattinger, D.H.: Questions of existence and uniqueness for hyperbolic equations with discontinuous coefficients. Trans. Am. Math. Soc. 132, 159–174 (1968)MathSciNetMATH
22.
Jovanovic, V., Rohde, C.: Error estimates for finite volume approximations of classical solutions for nonlinear systems of hyperbolic balance laws. SIAM J. Numer. Anal. 43, 2423–2449 (2006)MathSciNetMATH
23.
Kou, J., Sun, S., Wu, Y.: Mixed finite element-based fully conservative methods for simulating wormhole propagation. Comput. Methods Appl. Mech. Eng. 298, 279–302 (2016)MathSciNetMATH
24.
Li, X., Rui, H.: Block-centered finite difference method for simulating compressible wormhole propagation. J. Sci. Comput. 74, 1115–1145 (2018)MathSciNetMATH
25.
Li, X., Shu, C.-W., Yang, Y.: Local discontinuous Galerkin methods for Keller–Segel chemotaxis model. J. Sci. Comput. 73, 943–967 (2017)MathSciNetMATH
26.
Liu, M., Zhang, S., Mou, J., Zhou, F.: Wormhole propagation behavior under reservoir condition in carbonate acidizing. Transp. Porous Media 96, 203–220 (2013)
27.
Liu, W., Cui, J.: A two-grid block-centered finite difference algorithm for nonlinear compressible Darcy–Forchheimer model in porous media. J. Sci. Computi. 74, 1786–1815 (2018)MathSciNetMATH
28.
Mauran, S., Rigaud, L., Coudevylle, O.: Application of the Carman–Kozeny correlation to a highporosity and anisotropic consolidated medium: the compressed expanded natural graphite. Transp. Porous Media 43, 355–376 (2001)
29.
Ohlberger, M., Vovelle, J.: Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method. Math. Comput. 75, 113–150 (2006)MathSciNetMATH
30.
Oden, J.T., Wu, W., Ainsworth, M.: An a posteriori error estimate for finite element approximations of the Navier–Stokes equations. Comput. Methods Appl. Mech. Eng. 111, 185–202 (1994)MathSciNetMATH
31.
Pan, H., Rui, H.: A mixed element method for Darcy–Forchheimer incompressible miscible displacement problem. Comput. Methods Appl. Mech. Eng. 264, 1–11 (2013)MathSciNetMATH
32.
Pan, H., Rui, H.: Mixed element method for two-dimensional Darcy–Forchheimer model. J. Sci. Comput. 52, 563–587 (2012)MathSciNetMATH
33.
Panga, M.K.R., Ziauddin, M.: Two-scale continuum model for simulation of wormholes in carbonate acidization. AIChE J. 51, 3231–3248 (2005)
34.
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. 27, 995–1013 (2005)MathSciNetMATH
35.
Reed, W.H., Hill, T.R.: Triangular mesh method for the neutron transport equation. Technical report LA-UR-73-479, Los Alamos Scientific Laboratory, Los Alamos, NM (1973)
36.
Rui, H., Liu, W.: A two-grid block-centered finite difference method for Darcy–Forchheimer flow in porous media. SIAM J. Numer. Anal. 53, 1941–1962 (2015)MathSciNetMATH
37.
Rui, H., Pan, H.: A block-centered finite difference method for slightly compressible Darcy–Forchheimer flow in porous media. J. Sci. Comput. 73, 70–92 (2017)MathSciNetMATH
38.
Ruth, D., Ma, H.: On the derivation of the Forchheimer equation by means of the averaging theorem. Transp. Porous Media 7, 255–264 (1992)
39.
Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439–471 (1988)MathSciNetMATH
40.
Smirnov, A.S., Fedorov, K.M., Shevelev, A.P.: Modeling the acidizing of a carbonate formation. Fluid Dyn. 45, 779–786 (2010)MATH
41.
Szymczak, P., Ladd, A.J.C.: Wormhole formation in dissolving fractures. J. Gophys. Res. 114, B06203 (2009)
42.
Tian, L., Xu, Y., Kuerten, J.G.M., Van der Vegt, J.J.W.: An h-adaptive local discontinuous Galerkin method for the Navier–Stokes–Korteweg equations. J. Comput. Phys. 319, 242–265 (2016)MathSciNetMATH
43.
Verfürth, R.: A posteriori error estimators for the Stokes equations. Numer. Math. 55, 309–325 (1989)MathSciNetMATH
44.
Verfürth, R.: A review of a posteriori error estimation techniques for elasticity problems. Comput. Methods Appl. Mech. Eng. 176, 419–440 (1999)MathSciNetMATH
45.
Vilsmeier, R., Hänel, D.: Adaptive methods on unstructured grids for Euler and Navier–Stokes equations. Comput. Fluids 22, 485–499 (1993)MATH
46.
Wang, H., Shu, C.-W., Zhang, Q.: Stability and error estimates of local discontinuous Galerkin methods with implicit–explicit time-marching for advection–diffusion problems. SIAM J. Numer. Anal. 53, 206–227 (2015)MathSciNetMATH
47.
Wang, H., Shu, C.-W., Zhang, Q.: Stability analysis and error estimates of local discontinuous Galerkin methods with implicit–explicit time-marching for nonlinear convection–diffusion problems. Appl. Math. Comput. 272, 237–258 (2016)MathSciNetMATH
48.
Wang, H., Wang, S., Zhang, Q., Shu, C.-W.: Local discontinuous Galerkin methods with implicit–explicit time marching for multi-dimensional convection–diffusion problems. ESAIM: M2AN 50, 1083–1105 (2016)MathSciNetMATH
49.
Wu, Y., Salama, A., Sun, S.: Parallel simulation of wormhole propagation with the Darcy–Brinkman–Forchheimer framework. Comput. Geotech. 69, 564–577 (2015)
50.
Xu, W., Liang, D., Rui, H.: A multipoint flux mixed finite element method for the compressible Darcy–Forchheimer models. Appl. Math. Comput. 315, 259–277 (2017)MathSciNetMATH
51.
Xu, Y., Shu, C.-W.: Local discontinuous Galerkin methods for nonlinear Schrödinger equations. J. Comput. Phys. 205, 72–97 (2005)MathSciNetMATH
52.
Xu, Y., Shu, C.-W.: Error estimates of the semi-discrete local discontinuous Galerkin method for nonlinear convection–diffusion and KdV equations. Comput. Methods Appl. Mech. Eng. 196, 3805–3822 (2007)MathSciNetMATH
53.
Xu, Z., Yang, Y., Guo, H.: High-order bound-preserving discontinuous Galerkin methods for wormhole propagation on triangular meshes. J. Comput. Phys. 390, 323–341 (2019)MathSciNet
54.
Yan, J., Shu, C.-W.: Local discontinuous Galerkin methods for partial differential equations with higher order derivatives. J. Sci. Comput. 17, 27–47 (2002)MathSciNetMATH
55.
Yan, J., Shu, C.-W.: A local discontinuous Galerkin method for KdV type equations. SIAM J. Numer. Anal. 40, 769–791 (2002)MathSciNetMATH
56.
Yang, Y., Shu, C.-W.: Analysis of optimal superconvergence of local discontinuous Galerkin method for one-dimensional linear parabolic equations. J. Comput. Math. 33, 323–340 (2015)MathSciNet
57.
Yu, F., Guo, H., Chuenjarern, N., Yang, Y.: Conservative local discontinuous Galerkin method for compressible miscible displacements in porous media. J. Sci. Comput. 73, 1249–1275 (2017)MathSciNetMATH
58.
Zhao, C., Hobbs, B.E., Hornb, P., Ord, A., Peng, S., Liu, L.: Theoretical and numerical analyses of chemical-dissolution front instability in fluid-saturated porous rocks. Int. J. Numer. Anal. Methods Geomech. 32, 1107–1130 (2008)MATH
59.
Zhao, Q., Rui, H., Liu, W.: Cell-centered finite difference method for the one-dimensional Forchheimer laws. Bull. Malays. Math. Sci. Soc. 40, 545–564 (2017)MathSciNetMATH
60.
Zhu, H., Qiu, J.: Adaptive Runge–Kutta discontinuous Galerkin methods using different indicators: one-dimensional case. J. Comput. Phys. 228, 6957–6976 (2009)MathSciNetMATH
61.
Zhu, H., Qiu, J.: An h-adaptive RKDG method with troubled-cell indicator for two-dimensional hyperbolic conservation laws. Adv. Comput. Math. 39, 445–463 (2013)MathSciNetMATH
Metadaten
Titel
An Adaptive Local Discontinuous Galerkin Method for Simulating Wormhole Propagation with Darcy–Forcheiner Model
verfasst von
Lulu Tian
Hui Guo
Rui Jia
Yang Yang
Publikationsdatum
01.02.2020
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-020-01135-x

Weitere Artikel der Ausgabe 2/2020

Journal of Scientific Computing 2/2020 Zur Ausgabe

OriginalPaper

Stability and Error Analysis of Operator Splitting Methods for American Options Under the Black–Scholes Model

OriginalPaper

Well-Balanced High-Order Finite Volume Methods for Systems of Balance Laws

OriginalPaper

A Characteristic-wise Alternative WENO-Z Finite Difference Scheme for Solving the Compressible Multicomponent Non-reactive Flows in the Overestimated Quasi-conservative Form

OriginalPaper

Optimal Truncations for Multivariate Fourier and Chebyshev Series: Mysteries of the Hyperbolic Cross: Part I: Bivariate Case

OriginalPaper

Asymptotic Analysis and Numerical Methods for Oscillatory Infinite Generalized Bessel Transforms with an Irregular Oscillator

OriginalPaper

Fast Construction of Forward Flow Maps using Eulerian Based Interpolation Schemes