A Heterogeneous Multi-scale Approach to Liquid-Vapour Flow with Phase Transition

• Applicant: Professor Dr. Christian Rohde
• Subject Area: Mathematics
• Term: from 2010 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 170470158

• Final Report Year: 2017

Final Report Abstract

The dynamics of a compressible homogeneous fluid, appearimg in a liquid and a vapour state, is characterized by completely different spatial scales in the bulk phases and in the vicinity of the phase interfaces. Most of the classical mathematical models and/or numerical methods for direct numerical simulation introduce a complex coupling of scales such that even advanced computational techniques do not suffice to give the necessary resolution for e.g. bubble dynamics on the relevant continuum-mechanical length scale. To overcome these difficulties by scale separation we propose a heterogeneous multiscale method. In this sense, the dynamics of the bulk phases on the macroscale domain are modeled by the compressible Euler equations as a macroscale model. The microscale model governs the phase transition dynamics. Following the idea of sharp interface modeling leads to generalized Riemann problems. This approach enables the direct simulation of compressible liquid-vapour flow such that phase transition and surface tension effects are included. The overall method can be applied to the simulation of resolved phase boundary phenomena as e.g. the oscillation of single bubbles. Major results of the research are new isothermal and non-isothermal Riemann solvers for the microscale problem and a moving-mesh finite volume method for the macroscale tracking of the phase boundary.

Publications

• Numerical Solution of Navier-Stokes-Korteweg Systems by Local Discontinuous Galerkin Methods in Multiple Space Dimensions, Appl. Math. Comput. 272, Part 2, 309-335 (2016)
  Diehl, D., Kremser, J., Kroner, D., and Rohde, C.
  (See online at https://doi.org/10.1016/j.amc.2015.09.080)
• A Finite Volume Method for Undercompressive Shock Waves in Two Space Dimensions, ESAIM Math. Model. Numer. Anal., 2017
  Chalons, C., Rohde, C, and Wiebe, M
  (See online at https://doi.org/10.1051/m2an/2017027)
• A Sharp Interface Method for Compressible Liquid-Vapor Flow with Phase Transition and Surface Tension, J. Comput. Phys. 336, 347-374 (2017)
  Fechter S., Munz, C.-D., Rohde, C., and Zeiler, C.
  (See online at https://doi.org/10.1016/j.jcp.2017.02.001)