This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics.
The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete l
evel. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.
The book is useful for researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.
PART
4. Hyperbolic Problems. David Iampietro, Frederic Daude, Pascal
Galon, and Jean-Marc Herard, A Weighted Splitting Approach For Low-Mach
Number Flows.-
Florence Hubert and Remi Tesson, Weno scheme for transport equation on
unstructured grids with a DDFV approach.- M.J. Castro, J.M. Gallardo and A.
Marquina, New types of Jacobian-free approximate Riemann solvers for
hyperbolic systems.- Charles Demay, Christian Bourdarias, Benot de Laage de
Meux, Stephane Gerbi and Jean-Marc Herard, A fractional step method to
simulate mixed flows in pipes with a compressible two-layer model.- Theo
Corot, A second order cell-centered scheme for Lagrangian hydrodynamics.-
Clement Colas, Martin Ferrand, Jean-Marc Herard, Erwan Le Coupanec and Xavier
Martin, An implicit integral formulation for the modeling of inviscid fluid
flows in domains containing obstacles.- Christophe Chalons and Maxime
Stauffert, A high-order Discontinuous Galerkin Lagrange Projection scheme for
the barotropic Euler equations.- Christophe Chalons, Regis Duvigneau and
Camilla Fiorini, Sensitivity analysis for the Euler equations in Lagrangian
coordinates.- Jooyoung Hahn, Karol Mikula, Peter Frolkovic, and Branislav
Basara, Semi-implicit level set method with inflow-based gradient in a
polyhedron mesh.- Thierry Goudon, Julie Llobell and Sebastian Minjeaud, A
staggered scheme for the Euler equations.- Christian Bourdarias, Stephane
Gerbi and Ralph Lteif, A numerical scheme for the propagation of internal
waves in an oceanographic model.- Hamza Boukili and Jean-Marc Herard, A
splitting scheme for three-phase flow models.- M. J Castro, C. Escalante and
T. Morales de Luna, Modelling and simulation of non-hydrostatic shallow
flows.- Svetlana Tokareva and Eleuterio Toro, A flux splitting method for the
Baer-Nunziato equations of compressible two-phase flow.- Mohamed Boubekeur
and Fayssal Benkhaldoun and Mohammed Seaid, GPU accelerated finite volume
methods for three-dimensional shallow water flows.- Ward Melis, Thomas Rey
and Giovanni Samaey, Projective integration for nonlinear BGK kinetic
equations.- Lei Zhang, Jean-Michel Ghidaglia and Anela Kumbaro, Asymptotic
preserving property of a semi-implicit method.- Sebastien Boyaval, A
Finite-Volume discretization of viscoelastic Saint-Venant equations for
FENE-P fluids.- David Coulette, Emmanuel Franck, Philippe Helluy, Michel
Mehrenberger, Laurent Navoret, Palindromic Discontinuous Galerkin Method.- M.
Lukacova-Medvidova, J. Rosemeier, P. Spichtinger and B. Wiebe, IMEX finite
volume methods for cloud simulation.- Raimund Burger and Ilja Kroker, Hybrid
stochastic Galerkin finite volumes for the diffusively corrected
Lighthill-Whitham-Richards traffic model.- Hamed Zakerzadeh, The RS-IMEX
scheme for the rotating shallow water equations with the Coriolis force.-
Emmanuel Audusse, Minh Hieu Do, Pascal Omnes, Yohan Penel, Analysis of
Apparent Topography scheme for the linear wave equation with Coriolis force.-
N. Assiouene, M-O. Bristeau, E. Godlewski, A. Mangeney, C. Pares and J.
Sainte-Marie, Application of a combined finite element - finite volume method
to a 2D non-hydrostatic shallow water problem.- Emanuela Abbate, Angelo Iollo
and Gabriella Puppo, A relaxation scheme for the simulation of low Mach
number flows.- Stefan Vater, Nicole Beisiegel and Jorn Behrens, Comparison of
wetting and drying between a RKDG2 method and classical FV based second-order
hydrostatic reconstruction.- Anja Jeschke, Stefan Vater and J¨orn Behrens, A
Discontinuous Galerkin Method for Non-Hydrostatic Shallow Water Flows.- Remi
Abgrall and Paola Bacigaluppi, Design of a Second-Order Fully Explicit
Residual Distribution Scheme for Compressible Multiphase Flows.- Martin
Campos Pinto, An Unstructured Forward-Backward Lagrangian Scheme for
Transport Problems.- Nicole Goutal, Minh-Hoang Le and Philippe Ung, A
Godunov-type scheme for Shallow Water equations dedicated to simulations of
overland flows on stepped slopes.- Dionysios Grapsas, Raphaele Herbin and
Jean-Claude Latche, Two models for the computation of laminar flames in dust
clouds.- Gregoire Pont, Pierre Brenner, High order finite volume scheme and
conservative grid overlapping technique for complex industrial
applications.- PART
5. Elliptic and Parabolic problems. Sarvesh Kumar,
Ricardo Ruiz-Baier, Ruchi Sandilya, Discontinuous finite volume element
methods for the optimal control of Brinkman equations.- L. Beaude, K.
Brenner, S. Lopez, R. Masson, F. Smai, Non-isothermal compositional two-phase
Darcy flow: formulation and outflow boundary condition.- Clement Cances,
Didier Granjeon, Nicolas Peton, Quang Huy Tran, and Sylvie Wolf, Numerical
scheme for a stratigraphic model with erosion constraint and nonlinear
gravity flux.- Christoph Erath and Robert Schorr, Comparison of adaptive
non-symmetric and three-field FVM-BEM coupling.- Thomas Fetzer, Christoph
Gruninger, Bernd Flemisch, Rainer Helmig, On the Conditions for Coupling Free
Flow and Porous-MediumFlow in a Finite Volume Framework.- Mario Ohlberger and
Felix Schindler, Non-Conforming Localized Model Reduction with Online
Enrichment: Towards Optimal Complexity in PDE constrained Optimization.- Hanz
Martin Cheng and Jerome Droniou, Combining the Hybrid Mimetic Mixed method
and the Eulerian Lagrangian Localised Adjoint Method for approximating
miscible flows in porous media.- Ambartsumyan, E. Khattatov and I. Yotov,
Mixed finite volume methods for linear elasticity.- Nabil Birgle, Roland
Masson and Laurent Trenty, A nonlinear domain decomposition method to couple
compositional gas liquid Darcy and free gas flows.- Jurgen Fuhrmann, Annegret
Glitzky and Matthias Liero, Hybrid Finite-Volume/Finite-Element Schemes for
p(x)-Laplace Thermistor Models.- E. Ahusborde, B. Amaziane and M. El Ossmani,
Finite Volume Scheme for Coupling TwoPhase Flow with Reactive Transport in
Porous Media.- Martin Schneider, Dennis Gl¨aser, Bernd Flemisch and Rainer
Helmig, Nonlinear finite-volume scheme forcomplex flow processes on
corner-point grids.- Daniil Svyatskiy and Konstantin Lipnikov, Consistent
nonlinear solver for solute transport in variably saturated porous media.-
Jan ten Thije Boonkkamp, Martijn Anthonissen and Ruben Kwant, A
two-dimensional complete flux scheme in local flow adapted coordinates.-
Birane Kane, Robert Kl¨ofkorn, Christoph Gersbacher, hp-Adaptive
Discontinuous Galerkin Methods for Porous Media Flow.- N. Kumar, J.H.M. ten
Thije Boonkkamp, B. Koren and A. Linke, A Nonlinear Flux Approximation Scheme
for the Viscous Burgers Equation.- Rene Beltman, Martijn Anthonissen and
Barry Koren, Mimetic Staggered Discretization of Incompressible Navier-Stokes
for Barycentric Dual Mesh.- Sebastien Boyaval, Guillaume Enchery, Riad
Sanchez and Quang Huy Tran, A reduced-basis approach to two-phase flow in
porous media.- S´ebastien Boyaval, Guillaume Ench´ery, Riad Sanchez and Quang
Huy Tran, On the capillary pressure in basin modeling.- Jurgen Fuhrmann,
Clemens Guhlke, A finite volume scheme for Nernst-Planck-Poisson systems with
ion size and solvation effects.- Vasiliy Kramarenko, Kirill Nikitin, and Yuri
Vassilevski, A nonlinear correction FV scheme for near-well regions.- Florent
Chave, Daniele A. Di Pietro and Fabien Marche, A Hybrid High-Order method for
the convective Cahn-Hilliard problem in mixed form.- Alexey Chernyshenko,
Maxim Olshahskii and Yuri Vassilevski, A hybrid finite volume finite
element method for modeling flows in fractured media.- Michele Botti, Daniele
A. Di Pietro, and Pierre Sochala, A nonconforming high-order method for
nonlinear poroelasticity.- Hanen Amor and Fayssal Benkhaldoun and Tarek
Ghoudi and Imad Kissami and Mohammed Seaid, New criteria for mesh adaptation
in finite volume simulation of planar ionization wave front
propagation.- Author Index.
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