Springer Proceedings in Mathematics & Statistics Jürgen Fuhrmann Mario Ohlberger Christian Rohde Editors Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects FVCA 7, Berlin, June 2014 Springer Proceedings in Mathematics & Statistics Volume 77 For furthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including OR and optimization. In addition to an overall evaluation of the interest, scientific quality, and timeliness of each proposal at the hands of the publisher,individualcontributionsareallrefereedtothehighqualitystandardsof leading journals in the field. Thus, this series provides the research community with well-edited,authoritativereports ondevelopments inthe mostexciting areas of mathematical and statistical research today. Jürgen Fuhrmann Mario Ohlberger • Christian Rohde Editors Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects FVCA 7, Berlin, June 2014 123 Editors JürgenFuhrmann Christian Rohde Weierstrass Institute forApplied Instituteof AppliedAnalysis Analysis andStochastics andNumerical Simulation Berlin Universityof Stuttgart Germany Stuttgart Germany Mario Ohlberger InstituteforComputational and AppliedMathematics andCenter forNonlinear Sciences(CeNoS) Universityof Münster Münster Germany ISSN 2194-1009 ISSN 2194-1017 (electronic) ISBN 978-3-319-05683-8 ISBN 978-3-319-05684-5 (eBook) DOI 10.1007/978-3-319-05684-5 Springer ChamHeidelberg New YorkDordrecht London LibraryofCongressControlNumber:2014938474 MathematicsSubjectClassification:65-06,65Mxx,65Nxx,76xx,78xx,85-08,86-08,92-08 (cid:2)SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface The finite volume method in its various forms is a discretization technique for partial differential equations based on the fundamental physical principle of conservation. It has been used successfully in many applications including fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, and semiconductor theory. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties including maximum principles, dissipativity, monotone decay of the free energy, or asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of con- tinuousproblemsatthediscretelevel.Thisstructuralapproachtothediscretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The triennial series of conferences ‘‘International Symposium on Finite VolumesforComplexApplications—ProblemsandPerspectives(FVCA)’’brings together mathematicians, physicists, and engineers interested in this kind of physically motivated discretizations. Contributions to the further advancement of the theoretical understanding of suitable finite volume, finite element, discontin- uous Galerkin and other discretization schemes, and the exploration of new application fields have been welcomed. Previous conferences on this series have been held in Rouen (1996), Duisburg (1999), Porquerolles (2002), Marrakech (2005), Aussois (2008), and Prague (2011). The present volumes contain the invited and contributed papers presented as posters or talks at the Seventh International Symposium on Finite Volumes for Complex Applications held in Berlin on June 15–20, 2014. The contributions in the first volume deal with theoretical aspects of the method. They focus on topics like preservation of physical properties on the discrete level, convergence, stability and error analysis, physically consistent coupling between discretizations for different processes, connections to other discretization methods, relationship between grids and discretization schemes, complex geometries and adaptivity shock waves and other flow discontinuities, new and existing schemes and their limitations, bottlenecks in the solution of large-scale problems. v vi Preface As described, finite volume and related methods are of large practical value, which is demonstrated by the contributions to the second volume of the proceed- ings. Application fields include atmosphere and ocean modeling, chemical engi- neering and combustion energy generation and storage, electro-reaction-diffusion systems,and porous media. The volume editors thank the authors for their high-quality contributions, the members of the program committee for supporting the organization of the review process,andallreviewersfortheirthoroughworkontheevaluationofeachofthe contributions. The production of the proceedings was continuously supported by the Editor’s team at Springer Verlag. Without the financial contributions of the Deutsche Forschungsgemeinschaft (DFG), the Weierstrass Institute for Applied Analysis and Stochastics, the DFG Priority Program 1276 ‘‘Metström,’’ the Westfälische Universität Münster, the Stuttgart Research Centre for Simulation Technology (Simtech), and the Czech Technical University of Prague, the organization of the conference and the production of the proceedings would not have been possible. The Berlin Brandenburgische Akademie der Wissenschaften provided an impressive conference venue in the center of Berlin. Finally, we have to thank the local organizers and the staff at the Weierstrass InstituteforAppliedAnalysisandStochasticsforcarryingthemainorganizational burden and for providing a friendly atmosphere for the conference. March 2014 Jürgen Fuhrmann Mario Ohlberger Christian Rohde Organization Committees Organizing Committee Peter Bastian Robert Eymard Jürgen Fuhrmann Jirˇí Fürst Annegret Glitzky Volker John Rupert Klein Alexander Linke Mario Ohlberger Christian Rohde Jörn Sesterhenn Proceedings Committee Remi Abgrall Brahim Amaziane Boris Andreianov Peter Bastian Fayssal Benkhaldoun Franck Boyer Yves Coudière Andreas Dedner Vit Dolejsi Jerome Droniou Denis Dutykh Alexandre Ern Robert Eymard Jürgen Fuhrmann Jirˇí Fürst vii viii OrganizationCommittees Jan Giesselmann Annegret Glitzky Khaled Hassouni Christiane Helzel Jean-Marc Hérard Danielle Hilhorst Florence Hubert Volker John Rupert Klein Robert Kloefkorn Peter Knabner Alexander Linke Konstantin Lipnikov Andreas Meister Mario Ohlberger Christian Rohde Martin Rumpf Jörn Sesterhenn Martin Vohralik Petra Wittbold Contents Part I Invited Papers Low Mach Number Modeling of Stratified Flows. . . . . . . . . . . . . . . . 3 Ann Almgren, John Bell, Andrew Nonaka and Michael Zingale Entropy Method and Asymptotic Behaviours of Finite Volume Schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Claire Chainais-Hillairet Interpolated Pressure Laws in Two-Fluid Simulations and Hyperbolicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Philippe Helluy and Jonathan Jung Part II Theoretical Aspects An ALE Formulation for Explicit Runge-Kutta Residual Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Remi Abgrall, Luca Arpaia and Mario Ricchiuto Gradient Schemes for an Obstacle Problem. . . . . . . . . . . . . . . . . . . . 67 Yahya Alnashri and Jerome Droniou The Complete Flux Scheme in Cylindrical Coordinates . . . . . . . . . . . 77 M. J. H. Anthonissen and J. H. M. ten Thije Boonkkamp A Staggered Scheme with Non-conforming Refinement for the Navier-Stokes Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Fabrice Babik, Jean-Claude Latché, Bruno Piar and Khaled Saleh Consistency Analysis of a 1D Finite Volume Scheme for Barotropic Euler Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Florent Berthelin, Thierry Goudon and Sebastian Minjeaud ix