Exact and numerical solutions of the Riemann problem for a conservative model of compressible two-phase flows Thein, Ferdinand, Romenski, Evegeniy, Dumbser, Michael In: ArXiv e-prints, 2022 url, bibtex
@ARTICLE{Thein2022, title = {Exact and numerical solutions of the Riemann problem for a conservative model of compressible two-phase flows}, author = {Thein, Ferdinand and Romenski, Evegeniy and Dumbser, Michael}, journal = {ArXiv e-prints}, year = {2022}, archiveprefix = {arXiv}, url = {https://arxiv.org/abs/2203.12422}, doi = {10.48550/ARXIV.2203.12422} }
2021
On the invariant region for compressible Euler equations with a general equation of state Hailiang Liu, Ferdinand Thein In: Communications on Pure & Applied Analysis, 2021, 0 (1534-0392_2021084), url, bibtex
@ARTICLE{Liu2021, title = {On the invariant region for compressible Euler equations with a general equation of state}, journal = {Communications on Pure & Applied Analysis}, volume = {0}, number = {1534-0392_2021084}, pages = {}, year = {2021}, note = {}, issn = {1534-0392}, doi = {10.3934/cpaa.2021084}, url = {http://aimsciences.org//article/id/6e970dd5-e8e4-4508-80fc-6d7a7dbae298}, author = {Hailiang Liu and Ferdinand Thein}, keywords = {Euler equations","entropy","invariant region","equation of state","fundamental derivative}, abstract = {
The state space for solutions of the compressible Euler equations with a general equation of state is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. An invariant region of the resulting Euler system is identified and the convexity property of this region is justified by using only very minimal thermodynamical assumptions. Finally, we show how an invariant-region-preserving (IRP) limiter can be constructed for use in high order finite-volume type schemes to solve the compressible Euler equations with a general constitutive relation.
} }
2020
A Numerical Method for Two Phase Flows with Phase Transition Including Phase Creation Hantke, Maren, Thein, Ferdinand inbook url, bibtex
@INBOOK{Hantke2020, pages = {177--183}, title = {A Numerical Method for Two Phase Flows with Phase Transition Including Phase Creation}, publisher = {Springer International Publishing}, year = {2020}, editor = {Demidenko, Gennadii V. and Romenski, Evgeniy and Toro, Eleuterio and Dumbser, Michael}, author = {Hantke, Maren and Thein, Ferdinand}, address = {Cham}, abstract = {Two phase flows including phase transition, especially phase creation, with a sharp interface remain a challenging task for numerics. We consider the isothermal Euler equations with phase transition between a liquid and a vapour phase. The phase interface is modelled as a sharp interface, and the mass transfer across the phase boundary is modelled by a kinetic relation [6]. Existence and uniqueness results were proven in [2, 6]. We present a method to obtain the numerical solution for associated Riemann problems. In particular, we show how the cases of nucleation and cavitation may be treated. We will highlight the major difficulties and propose possible strategies to overcome these problems.}, booktitle = {Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov}, doi = {10.1007/978-3-030-38870-6_23}, isbn = {978-3-030-38870-6}, url = {https://doi.org/10.1007/978-3-030-38870-6_23} }
A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model Kemm, F., Gaburro, E., Thein, F., Dumbser, M. In: ArXiv e-prints, 2020 url, bibtex
@ARTICLE{Kemm2020, author = {{Kemm}, F., {Gaburro}, E., {Thein}, F., {Dumbser}, M.}, title = {{A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model}}, journal = {ArXiv e-prints}, year = {2020}, month = {}, adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170309431H}, archiveprefix = {arXiv}, eprint = {2001.10326}, primaryclass = {math.NA}, url = {https://arxiv.org/abs/2001.10326} }
A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model Friedemann Kemm, Elena Gaburro, Ferdinand Thein, Michael Dumbser In: Computers \& Fluids, 2020, 204, 104536url, bibtex
@ARTICLE{Kemm2020a, author = {Friedemann Kemm and Elena Gaburro and Ferdinand Thein and Michael Dumbser}, title = {A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model}, journal = {Computers \& Fluids}, year = {2020}, volume = {204}, pages = {104536}, abstract = {In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The mathematical model is a simplified case of the seven-equation Baer–Nunziato model of compressible multi-phase flows. The resulting governing PDE system is a nonlinear system of hyperbolic conservation laws with non-conservative products. The geometry of the solid bodies is simply specified via a scalar field that represents the volume fraction of the fluid present in each control volume. This allows the discretization of arbitrarily complex geometries on simple uniform or adaptive Cartesian meshes. Inside the solid bodies, the fluid volume fraction is zero, while it is unitary inside the fluid phase. Due to the diffuse interface nature of the model, the volume fraction function can assume any value between zero and one in mixed cells that are occupied by both, fluid and solid. We also prove that at the material interface, i.e. where the volume fraction jumps from unity to zero, the normal component of the fluid velocity assumes the value of the normal component of the solid velocity. This result can be directly derived from the governing equations, either via Riemann invariants or from the generalized Rankine Hugoniot conditions according to the theory of Dal Maso et al. (1995)[89], which justifies the use of a path-conservative approach for treating the non-conservative products. The governing partial differential equations of our new model are solved on simple uniform Cartesian grids via a high order path-conservative ADER discontinuous Galerkin (DG) finite element method with a posteriori sub-cell finite volume (FV) limiter. Since the numerical method is of the shock capturing type, the fluid-solid boundary is never explicitly tracked by the numerical method, neither via interface reconstruction, nor via mesh motion. The effectiveness of the proposed approach is tested on a set of different numerical test problems, including 1D Riemann problems as well as supersonic flows over fixed and moving rigid bodies.}, doi = {https://doi.org/10.1016/j.compfluid.2020.104536}, issn = {0045-7930}, keywords = {Diffuse interface model, Compressible flows over fixed and moving solids, Immersed boundary method for compressible flows, Arbitrary high-order discontinuous Galerkin schemes, A posteriori sub-cell finite volume limiter (MOOD), Path-conservative schemes for hyperbolic PDE with non-conservative products}, url = {http://www.sciencedirect.com/science/article/pii/S0045793020301080} }
2019
On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations Hantke, Maren, Thein, Ferdinand In: Entropy, 2019, 21url, bibtex
@ARTICLE{Hantke2019, author = {Hantke, Maren and Thein, Ferdinand}, title = {On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations}, journal = {Entropy}, year = {2019}, volume = {21}, number = {11}, abstract = {Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.}, article-number = {1039}, doi = {10.3390/e21111039}, issn = {1099-4300}, url = {https://www.mdpi.com/1099-4300/21/11/1039} }
A general existence result for isothermal two-phase flows with phase transition Hantke, Maren, Thein, Ferdinand In: Journal of Hyperbolic Differential Equations, 2019, 16 (04), 595-637url, bibtex
@ARTICLE{Hantke2019a, author = {Hantke, Maren and Thein, Ferdinand}, title = {A general existence result for isothermal two-phase flows with phase transition}, journal = {Journal of Hyperbolic Differential Equations}, year = {2019}, volume = {16}, pages = {595-637}, number = {04}, abstract = {Liquid–vapor flows with phase transitions have a wide range of applications. Isothermal two-phase flows described by a single set of isothermal Euler equations,where the mass transfer is modeled by a kinetic relation, have been investigated analytically in [M. Hantke, W. Dreyer and G. Warnecke, Exact solutions to the Riemann problem for compressible isothermal Euler equations for two-phase flows with and without phase transition, Quart. Appl. Math. 71(3) (2013) 509–540]. This work was restricted to liquid water and its vapor modeled by linear equations of state. The focus of this work lies on the generalization of the primary results to arbitrary substances, arbitrary equations of state and thus a more general kinetic relation. We prove existence and uniqueness results for Riemann problems. In particular, nucleation and cavitation are discussed.}, doi = {10.1142/S0219891619500206}, eprint = {https://doi.org/10.1142/S0219891619500206}, url = {https://doi.org/10.1142/S0219891619500206} }
2018
Results for Two Phase Flows with Phase Transition Thein, Ferdinand PhD Thesis, Otto-von-Guericke-Universität Magdeburg, 2018 pdf, url, bibtex
@PHDTHESIS{Thein2018, author = {Thein, Ferdinand}, title = {Results for Two Phase Flows with Phase Transition}, school = {Otto-von-Guericke-Universit{\"a}t Magdeburg}, year = {2018}, type = {PhD Thesis}, pdfurl = {/~thein/papers/diss_thein.pdf}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-12073} }
2017
A general existence result for isothermal two-phase flows with phase transition Hantke, M., Thein, F. In: ArXiv e-prints, 2017 url, bibtex
@ARTICLE{Hantke2017, author = {{Hantke}, M. and {Thein}, F.}, title = {{A general existence result for isothermal two-phase flows with phase transition}}, journal = {ArXiv e-prints}, year = {2017}, month = {}, adsnote = {Provided by the SAO/NASA Astrophysics Data System}, adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170309431H}, archiveprefix = {arXiv}, eprint = {1703.09431}, keywords = {Mathematics - Analysis of PDEs, 76T10, 35L65, 35Q31, 82C26}, primaryclass = {math.AP}, url = {https://arxiv.org/pdf/1703.09431.pdf} }
2016
Singular and selfsimilar solutions for Euler equations with phase transitions Thein, Ferdinand, Hantke, Maren In: Bulletin of the Brazilian Mathematical Society, New Series, 2016, 47 (2), 779--786url, bibtex
@ARTICLE{Thein2016, author = {Thein, Ferdinand and Hantke, Maren}, title = {Singular and selfsimilar solutions for Euler equations with phase transitions}, journal = {Bulletin of the Brazilian Mathematical Society, New Series}, year = {2016}, volume = {47}, pages = {779--786}, number = {2}, abstract = {Riemann problems for the full set of Euler equations for two phases with phase transition are considered. Based on the assumptions across the phase boundary kinetic relations to describe the mass transfer between the phase are derived from the second law of thermodynamics. Self-similar as well as singular solutions can be constructed. For both cases the structure of the solution is discussed.}, doi = {10.1007/s00574-016-0185-3}, issn = {1678-7714}, url = {http://dx.doi.org/10.1007/s00574-016-0185-3} }
2015
Why condensation by compression in pure water vapor cannot occur in an approach based on Euler equations Maren Hantke, Ferdinand Thein In: Quart. Appl. Math., 2015, 73 (3), 575-591url, bibtex
@ARTICLE{Hantke2015a, author = {Maren Hantke and Ferdinand Thein}, title = {Why condensation by compression in pure water vapor cannot occur in an approach based on Euler equations}, journal = {Quart. Appl. Math.}, year = {2015}, volume = {73}, pages = {575-591}, number = {3}, month = {September}, abstract = {Phase transitions are in the focus of the modeling of multiphase flows. A large number of models are available to describe such processes. We consider several different two phase models that are based on the Euler equations of compressible fluid flows and that take into account phase transitions between a liquid phase and its vapor. Especially we consider the flow of liquid water and water vapor. We give a mathematical proof that all these models are not able to describe the process of condensation by compression. This behavior is in agreement with observations in experiments that simulate adiabatic flows and shows that the Euler equations give a fairly good description of the process. The mathematical proof is valid for the official standard IAPWS-IF97 for water and for any other good equation of state. Also the opposite case of expanding the liquid phase will be discussed.}, doi = {http://dx.doi.org/10.1090/qam/1393}, keywords = {MSC (2010): Primary 35Q31, 82B26, 82C26, 80A22, 76B10}, url = {http://www.ams.org/journals/qam/2015-73-03/S0033-569X-2015-01393-9/} }
2014
Numerical solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition Maren Hantke, Ferdinand Thein In: Hyperbolic Problems, Theory, Numerics, Applications, Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson (eds.), Applied Mathematics 8, American Institute of Mathematical Sciences,2014, 651 - 658url, bibtex
@INPROCEEDINGS{MarenHantke2014, author = {Maren Hantke, Ferdinand Thein}, title = {Numerical solutions to the Riemann problem for compressible isothermal Euler equations for two phase flows with and without phase transition}, booktitle = {Hyperbolic Problems, Theory, Numerics, Applications}, year = {2014}, editor = {Fabio Ancona, Alberto Bressan, Pierangelo Marcati, Andrea Marson}, volume = {8}, series = {Applied Mathematics}, pages = {651 - 658}, publisher = {American Institute of Mathematical Sciences}, url = {http://aimsciences.org/books/am/AMVol8.html} }
2012
On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM) Volker John, Ferdinand Thein In: Chemical Engineering Science, 2012, 75 (0), 327 - 333url, bibtex
@ARTICLE{John2012327, author = {Volker John and Ferdinand Thein}, title = {On the efficiency and robustness of the core routine of the quadrature method of moments (QMOM)}, journal = {Chemical Engineering Science}, year = {2012}, volume = {75}, pages = {327 - 333}, number = {0}, doi = {10.1016/j.ces.2012.03.024}, issn = {0009-2509}, keywords = {Quadrature method of moments}, url = {http://www.sciencedirect.com/science/article/pii/S000925091200187X} }
2011
On the Efficiency and Robustness of the Core Routine of the Quadrature Methods of Moments (QMOM) Ferdinand Thein Diploma Thesis, Otto-von-Guericke-Universität Magdeburg, 2011 pdf, url, bibtex
@MASTERSTHESIS{Thein11, author = {Ferdinand Thein}, title = {On the Efficiency and Robustness of the Core Routine of the Quadrature Methods of Moments (QMOM)}, school = {Otto-von-Guericke-Universität Magdeburg}, year = {2011}, type = {Diploma Thesis}, pdfurl = {/~thein/papers/diplom_thein.pdf}, url = {http://www.math.uni-magdeburg.de/~thein/papers/diplom_thein.pdf} }