parDG

Higher-order schemes for simulation of compressible liquid-vapor flows with phase change. With CD-ROM. The aim of this thesis is the numerical simulation of two-phase flows undergoing dynamical phase transitions. Such flows are of highly industrial interest since collapsing cavitation bubbles are responsible for erosion damage on ship propellers, pumps and turbines. Lord Rayleigh recognized in 1917 that collapsing vapor bubbles can cause this kind of damage. In this work the flow is modeled by the Navier-Stokes-Korteweg equations which belong to the class of Diffuse-Interface models. We develop efficient and reliable numerical schemes based on modern numerical techniques such as higher order Discontinuous Galerkin schemes, local mesh adaption, parallelization and load-balancing in multiple space dimensions. We provide a software package (written in C++) for the discretization of general time dependent partial differential equations. The discretization of the Navier-Stokes-Korteweg model is done on the basis of this package. For the validation of the resulting schemes special (quasi-exact) solutions are constructed. Several benchmarks show the efficiency and reliability of the methods. However, physical experiments are not available on the length scale that can be simulated and therefore the results cannot compared to real world data.


References in zbMATH (referenced in 16 articles , 1 standard article )

Showing results 1 to 16 of 16.
Sorted by year (citations)

  1. Park, Keunsoo; Gerritsma, Marc; Fernandino, Maria: (C^1) continuous (h)-adaptive least-squares spectral element method for phase-field models (2018)
  2. Chertock, Alina; Degond, Pierre; Neusser, Jochen: An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations (2017)
  3. Park, Keunsoo; Fernandino, Maria; Dorao, Carlos A.; Gerritsma, Marc: The least-squares spectral element method for phase-field models for isothermal fluid mixture (2017)
  4. Bueno, Jesus; Gomez, Hector: Liquid-vapor transformations with surfactants. Phase-field model and isogeometric analysis (2016)
  5. Diehl, Dennis; Kremser, Jenny; Kröner, Dietmar; Rohde, Christian: Numerical solution of Navier-Stokes-Korteweg systems by local discontinuous Galerkin methods in multiple space dimensions (2016)
  6. Giesselmann, Jan; Pryer, Tristan: Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics (2016)
  7. Tian, Lulu; Xu, Yan; Kuerten, J. G. M.; van der Vegt, J. J. W.: An (h)-adaptive local discontinuous Galerkin method for the Navier-Stokes-Korteweg equations (2016)
  8. Bueno, Jesus; Bona-Casas, Carles; Bazilevs, Yuri; Gomez, Hector: Interaction of complex fluids and solids: theory, algorithms and application to phase-change-driven implosion (2015)
  9. Tian, Lulu; Xu, Yan; Kuerten, J. G. M.; van der Vegt, J. J. W.: A local discontinuous Galerkin method for the (non)-isothermal Navier-Stokes-Korteweg equations (2015)
  10. Giesselmann, Jan; Makridakis, Charalambos; Pryer, Tristan: Energy consistent discontinuous Galerkin methods for the Navier-Stokes-Korteweg system (2014)
  11. Liu, Ju; Gomez, Hector; Evans, John A.; Hughes, Thomas J. R.; Landis, Chad M.: Functional entropy variables: a new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier-Stokes-Korteweg equations (2013)
  12. Aki, Gonca; Daube, Johannes; Dreyer, Wolfgang; Giesselmann, Jan; Kränkel, Mirko; Kraus, Christiane: A diffuse interface model for quasi-incompressible flows: sharp interface limits and numerics (2012)
  13. Hermsdörfer, Katharina; Kraus, Christiane; Kröner, Dietmar: Interface conditions for limits of the Navier-Stokes-Korteweg model (2011)
  14. Dedner, Andreas; Klöfkorn, Robert; Nolte, Martin; Ohlberger, Mario: A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module (2010)
  15. Gomez, Hector; Hughes, Thomas J. R.; Nogueira, Xesús; Calo, Victor M.: Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations (2010)
  16. Diehl, Dennis: Higher-order schemes for simulation of compressible liquid-vapor flows with phase change. With CD-ROM. (2007)