The computation of nonclassical shock waves with a heterogeneous multiscale method

  • Received: 01 January 2010 Revised: 01 May 2010
  • Primary: 35L65.

  • We consider weak solutions of hyperbolic conservation laws as singular limits of solutions for associated complex regularized problems. We are interested in situations such that undercompressive (Non-Laxian) shock waves occur in the limit. In this setting one can view the conservation law as a macroscale formulation while the regularization can be understood as the microscale model.
       With this point of view it appears natural to solve the macroscale model by a heterogeneous multiscale approach in the sense of E&Engquist[7]. We introduce a new mass-conserving numerical method based on this concept and test it on scalar model problems. This includes applications from phase transition theory as well as from two-phase flow in porous media.

    Citation: Frederike Kissling, Christian Rohde. The computation of nonclassical shock waves with a heterogeneousmultiscale method[J]. Networks and Heterogeneous Media, 2010, 5(3): 661-674. doi: 10.3934/nhm.2010.5.661

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  • We consider weak solutions of hyperbolic conservation laws as singular limits of solutions for associated complex regularized problems. We are interested in situations such that undercompressive (Non-Laxian) shock waves occur in the limit. In this setting one can view the conservation law as a macroscale formulation while the regularization can be understood as the microscale model.
       With this point of view it appears natural to solve the macroscale model by a heterogeneous multiscale approach in the sense of E&Engquist[7]. We introduce a new mass-conserving numerical method based on this concept and test it on scalar model problems. This includes applications from phase transition theory as well as from two-phase flow in porous media.


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