Modelling and Computation of Shocks and Interfaces

Livrables

List of Summer - Winter Schools/Invited lecture series/Transferable skills activities

Report of ESRs secondments

Report on the scientific results related to Measure Valued Solutions and Uncertainty Quantification and in particular in connection to -- Construction, analysis and assessment of computational methods for measure valued solutions. -- Convergence, scalability to realistic problems, and computational efficiency of Uncertainty Quantification for HCD-PDEs. Analytical issues for stochastic HCD-PDEs. The report will include references to related papers, preprints and PhD theses.

Progress on Research Theme 4

Progress report on RT4 : Report on the scientific progress related to Applications and in particular in connection to Modeling, computation and analysis for problems in Aerodynamics (compressible Euler and Navier-Stokes equations), Geophysics and Environmental science, Oil and gas exploration, Materials (cavitation, fracture, shear bands and modelling the dynamics of dislocations, mechanical properties of cells). The report will include references to related papers and preprints if available.

Results on Research Theme 2

Report on the scientific results related to Propagating Interfaces and in particular in connection to -- Propagating phase boundaries and small scale dependent shock waves. Analytical and computational issues related to small scale dependent shock waves for non-convex hyperbolic systems and mixed type systems. -- Study of shock waves in hydrodynamic type systems where the dominant regularization mechanism is a small dispersion. The numerical resolution of these waves and its connection to propagating interfaces at atomistic level will be investigated. The report will include references to related papers, preprints and PhD theses.

Progress on Research Theme 3

Progress report on RT3 : Report on the scientific progress related to Models and Methods across scales and in particular in connection to -- Multiscale methods. Methods Design and analysis of adaptive methods for discretIzing HCD-PDEs -- Design, computation and analysis of coupled models across scales. Time dependent coupling and connection to hyperbolic and nearly hyperbolic PDEs. The report will include references to related papers and preprints if available.

Results on Research Theme 4

Report on the scientific results related to Applications and in particular in connection to Modeling, computation and analysis for problems in Aerodynamics (compressible Euler and Navier-Stokes equations), Geophysics and Environmental science, Oil and gas exploration, Materials (cavitation, fracture, shear bands and modelling the dynamics of dislocations, mechanical properties of cells). The report will include references to related papers, preprints and PhD theses.

Dissemination-2

List of conference participation

Progress on Research Theme 2

Progress report on RT2 : Report on the scientific progress related to Propagating Interfaces and in particular in connection to -- Propagating phase boundaries and small scale dependent shock waves. Analytical and computational issues related to small scale dependent shock waves for non-convex hyperbolic systems and mixed type systems. -- Study of shock waves in hydrodynamic type systems where the dominant regularization mechanism is a small dispersion. The numerical resolution of these waves and its connection to propagating interfaces at atomistic level will be investigated. The report will include references to related papers and preprints if available.

Results on Research Theme 3

Report on the scientific results related to Models and Methods across scales and in particular in connection to -- Multiscale methods. Methods Design and analysis of adaptive methods for discretIzing HCD-PDEs -- Design, computation and analysis of coupled models across scales. Time dependent coupling and connection to hyperbolic and nearly hyperbolic PDEs. The report will include references to related papers, preprints and PhD theses.

Progress on Research Theme 1

Progress report on RT1 : Report on the scientific progress related to Measure Valued Solutions and Uncertainty Quantification and in particular in connection to -- Construction, analysis and assessment of computational methods for measure valued solutions. -- Convergence, scalability to realistic problems, and computational efficiency of Uncertainty Quantification for HCD-PDEs. Analytical issues for stochastic HCD-PDEs. The report will include references to related papers and preprints if available.

Supervisory Board

Supervisory Board of the network. Due by month 2.

Management-1

Contract of SA

Midterm Review Meeting

Dissemination-1

Website/Preprint server

Publications

Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

Auteurs: Georgios Grekas, Maria Proestaki, Phoebus Rosakis, Jacob Notbohm, Charalambos Makridakis, Guruswami Ravichandran
Publié dans: Journal of The Royal Society Interface, Numéro 18/175, 2021, ISSN 1742-5662
Éditeur: The Royal Society
DOI: 10.1098/rsif.2020.0823

Flow solutions of transport equations

Auteurs: Sholeh Karimghasemi, Siegfried Müller, Michael Westdickenberg
Publié dans: Communications in Partial Differential Equations, Numéro 46/1, 2021, Page(s) 98-134, ISSN 0360-5302
Éditeur: Marcel Dekker Inc.
DOI: 10.1080/03605302.2020.1831018

The Optimal Convergence Rate of Monotone Schemes for Conservation Laws in the Wasserstein Distance

Auteurs: Adrian M. Ruf, Espen Sande, Susanne Solem
Publié dans: Journal of Scientific Computing, Numéro 80/3, 2019, Page(s) 1764-1776, ISSN 0885-7474
Éditeur: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-00996-1

High Order Asymptotic Preserving Deferred Correction Implicit-Explicit Schemes for Kinetic Models

Auteurs: Rémi Abgrall, Davide Torlo
Publié dans: SIAM Journal on Scientific Computing, Numéro 42/3, 2020, Page(s) B816-B845, ISSN 1064-8275
Éditeur: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m128973x

Convergence of second-order, entropy stable methods for multi-dimensional conservation laws

Auteurs: Neelabja Chatterjee, Ulrik Skre Fjordholm
Publié dans: ESAIM: Mathematical Modelling and Numerical Analysis, Numéro 54/4, 2020, Page(s) 1415-1428, ISSN 0764-583X
Éditeur: EDP Sciences
DOI: 10.1051/m2an/2019090

Numerical investigations into a model of partially incompressible two-phase flow in pipes

Auteurs: Nils Henrik Risebro, Adrian M. Ruf
Publié dans: SeMA Journal, Numéro 77/2, 2020, Page(s) 143-159, ISSN 2254-3902
Éditeur: Springer
DOI: 10.1007/s40324-019-00207-9

Derivation of a Linearised Elasticity Model from Singularly Perturbed Multiwell Energy Functionals

Auteurs: Roberto Alicandro, Gianni Dal Maso, Giuliano Lazzaroni, Mariapia Palombaro
Publié dans: Archive for Rational Mechanics and Analysis, Numéro 230/1, 2018, Page(s) 1-45, ISSN 0003-9527
Éditeur: Springer Verlag
DOI: 10.1007/s00205-018-1240-6

A new class of entropy stable schemes for hyperbolic systems: Finite element methods

Auteurs: Ioannis Gkanis, Charalambos G. Makridakis
Publié dans: Mathematics of Computation, 2021, Page(s) 1, ISSN 0025-5718
Éditeur: American Mathematical Society
DOI: 10.1090/mcom/3617

Models for Dense Multilane Vehicular Traffic

Auteurs: Helge Holden, Nils Henrik Risebro
Publié dans: SIAM Journal on Mathematical Analysis, Numéro 51/5, 2019, Page(s) 3694-3713, ISSN 0036-1410
Éditeur: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m124318x

Formulation and convergence of the finite volume method for conservation laws on spacetimes with boundary

Auteurs: Jan Giesselmann, Philippe G. LeFloch
Publié dans: Numerische Mathematik, Numéro 144/4, 2020, Page(s) 751-785, ISSN 0029-599X
Éditeur: Springer Verlag
DOI: 10.1007/s00211-020-01101-7

The inverse-deformation approach to fracture

Auteurs: Phoebus Rosakis, Timothy J. Healey, Uğur Alyanak
Publié dans: Journal of the Mechanics and Physics of Solids, Numéro 150, 2021, Page(s) 104352, ISSN 0022-5096
Éditeur: Pergamon Press Ltd.
DOI: 10.1016/j.jmps.2021.104352

An entropy satisfying two-speed relaxation system for the barotropic Euler equations: application to the numerical approximation of low Mach number flows

Auteurs: François Bouchut, Christophe Chalons, Sébastien Guisset
Publié dans: Numerische Mathematik, Numéro 145/1, 2020, Page(s) 35-76, ISSN 0029-599X
Éditeur: Springer Verlag
DOI: 10.1007/s00211-020-01111-5

A robust model for rapidly varying flows over movable bottom with suspended and bedload transport: Modelling and numerical approach

Auteurs: J.C. González-Aguirre, M.J. Castro, T. Morales de Luna
Publié dans: Advances in Water Resources, Numéro 140, 2020, Page(s) 103575, ISSN 0309-1708
Éditeur: Pergamon Press Ltd.
DOI: 10.1016/j.advwatres.2020.103575

Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

Auteurs: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Publié dans: Discrete & Continuous Dynamical Systems - A, Numéro 39/11, 2019, Page(s) 6175-6206, ISSN 1553-5231
Éditeur: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019269

Lax-Wendroff Approximate Taylor Methods with Fast and Optimized Weighted Essentially Non-oscillatory Reconstructions

Auteurs: H. Carrillo, C. Parés, D. Zorío
Publié dans: Journal of Scientific Computing, Numéro 86/1, 2021, ISSN 0885-7474
Éditeur: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-020-01380-0

Asymptotic Structure of Cosmological Burgers Flows in One and Two Space Dimensions: A Numerical Study

Auteurs: Yangyang Cao
Publié dans: Communications in Computational Physics, Numéro 29/2, 2020, Page(s) 472-509, ISSN 1815-2406
Éditeur: Global Science Press
DOI: 10.4208/cicp.oa-2020-0033

Global Evolution of the U(1) Higgs Boson: Nonlinear Stability and Uniform Energy Bounds

Auteurs: Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Publié dans: Annales Henri Poincaré, 2020, ISSN 1424-0637
Éditeur: Birkhauser Verlag
DOI: 10.1007/s00023-020-00955-9

A well balanced diffuse interface method for complex nonhydrostatic free surface flows

Auteurs: Elena Gaburro; Manuel J. Castro; Michael Dumbser
Publié dans: Science Direct, Numéro Volume 175, 15 October 2018, 2018, Page(s) Pages 180 - 198, ISSN 0045-7930
Éditeur: Pergamon Press Ltd.
DOI: 10.1016/j.compfluid.2018.08.013

Global well-posedness and twist-wave solutions for the inertial Qian–Sheng model of liquid crystals

Auteurs: Francesco De Anna, Arghir Zarnescu
Publié dans: Journal of Differential Equations, Numéro 264/2, 2018, Page(s) 1080-1118, ISSN 0022-0396
Éditeur: Academic Press
DOI: 10.1016/j.jde.2017.09.031

Convergence of a full discretization for a second-order nonlinear elastodynamic equation in isotropic and anisotropic Orlicz spaces

Auteurs: A. M. Ruf
Publié dans: Zeitschrift für angewandte Mathematik und Physik, Numéro 68/5, 2017, ISSN 0044-2275
Éditeur: Birkhauser Verlag
DOI: 10.1007/s00033-017-0863-z

Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

Auteurs: Elena Gaburro, Manuel J Castro, Michael Dumbser
Publié dans: Monthly Notices of the Royal Astronomical Society, Numéro 477/2, 2018, Page(s) 2251-2275, ISSN 0035-8711
Éditeur: Blackwell Publishing Inc.
DOI: 10.1093/mnras/sty542

Convergence of the finite volume method on a Schwarzschild background

Auteurs: Shijie Dong, Philippe G. LeFloch
Publié dans: ESAIM: Mathematical Modelling and Numerical Analysis, Numéro 53/5, 2019, Page(s) 1459-1476, ISSN 0764-583X
Éditeur: EDP Sciences
DOI: 10.1051/m2an/2019037

Compact Approximate Taylor Methods for Systems of Conservation Laws

Auteurs: H. Carrillo, C. Parés
Publié dans: Journal of Scientific Computing, Numéro 80/3, 2019, Page(s) 1832-1866, ISSN 0885-7474
Éditeur: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-01005-1

Linearly implicit all Mach number shock capturing schemes for the Euler equations

Auteurs: Stavros Avgerinos, Florian Bernard, Angelo Iollo, Giovanni Russo
Publié dans: Journal of Computational Physics, Numéro 393, 2019, Page(s) 278-312, ISSN 0021-9991
Éditeur: Academic Press
DOI: 10.1016/j.jcp.2019.04.020

Well-posedness of the Initial Value Problem for the Ostrovsky–Hunter Equation with Spatially Dependent Flux

Auteurs: G. M. Coclite, N. Chatterjee, N. H. Risebro
Publié dans: Milan Journal of Mathematics, Numéro 87/2, 2019, Page(s) 283-301, ISSN 1424-9286
Éditeur: Birkhauser Verlag
DOI: 10.1007/s00032-019-00302-6

Stability of a coupled wave-Klein-Gordon system with quadratic nonlinearities

Auteurs: Shijie Dong, Zoe Wyatt
Publié dans: Journal of Differential Equations, Numéro 269/9, 2020, Page(s) 7470-7497, ISSN 0022-0396
Éditeur: Academic Press
DOI: 10.1016/j.jde.2020.05.019

Reprint of: Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes

Auteurs: Elena Gaburro, Michael Dumbser, Manuel J. Castro
Publié dans: Computers & Fluids, Numéro 169, 2018, Page(s) 263-284, ISSN 0045-7930
Éditeur: Pergamon Press Ltd.
DOI: 10.1016/j.compfluid.2018.03.051

A symmetrizable extension of polyconvex thermoelasticity and applications to zero-viscosity limits and weak-strong uniqueness

Auteurs: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Publié dans: Communications in Partial Differential Equations, Numéro 43/7, 2018, Page(s) 1019-1050, ISSN 0360-5302
Éditeur: Marcel Dekker Inc.
DOI: 10.1080/03605302.2018.1456551

Weak solution of the merged mathematical equations of the polluted atmosphere

Auteurs: Donatella Donatelli, Nóra Juhász
Publié dans: Mathematical Methods in the Applied Sciences, Numéro 43/15, 2020, Page(s) 9245-9261, ISSN 0170-4214
Éditeur: John Wiley & Sons Inc.
DOI: 10.1002/mma.6618

Weak dissipative solutions to a free-boundary problem for finitely extensible bead-spring chain molecules: Variable viscosity coefficients

Auteurs: Donatella Donatelli, Tessa Thorsen, Konstantina Trivisa
Publié dans: Kinetic & Related Models, Numéro 13/5, 2020, Page(s) 1047-1070, ISSN 1937-5077
Éditeur: American Institute of Mathematical Sciences
DOI: 10.3934/krm.2020037

All Mach Number Second Order Semi-implicit Scheme for the Euler Equations of Gas Dynamics

Auteurs: S. Boscarino, G. Russo, L. Scandurra
Publié dans: Journal of Scientific Computing, Numéro 77/2, 2018, Page(s) 850-884, ISSN 0885-7474
Éditeur: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-018-0731-9

A convergent finite difference scheme for the Ostrovsky--Hunter equation with Dirichlet boundary conditions

Auteurs: Johanna Ridder, Adrian Montgomery Ruf
Publié dans: BIT Numerical Mathematics, Numéro 59, (2019), 2019, Page(s) pages775–796, ISSN 0006-3835
Éditeur: Springer
DOI: 10.1007/s10543-019-00746-7

A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws

Auteurs: N Chatterjee, U S Fjordholm
Publié dans: IMA Journal of Numerical Analysis, Numéro 40/1, 2018, Page(s) 405-421, ISSN 0272-4979
Éditeur: Oxford University Press
DOI: 10.1093/imanum/dry074

Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux

Auteurs: Jayesh Badwaik, Adrian M. Ruf
Publié dans: SIAM Journal on Numerical Analysis, Numéro 58/1, 2020, Page(s) 607-629, ISSN 0036-1429
Éditeur: Society for Industrial and Applied Mathematics
DOI: 10.1137/19M1283276

On a free boundary problem for finitely extensible bead-spring chain molecules in dilute polymers

Auteurs: Donatella Donatelli, Konstantina Trivisa
Publié dans: Journal of Mathematical Analysis and Applications, Numéro 482/1, 2020, Page(s) 123527, ISSN 0022-247X
Éditeur: Academic Press
DOI: 10.1016/j.jmaa.2019.123527

Stability of Quasilinear Waves in $$1+1$$1+1 Dimension Under Null Condition

Auteurs: Shijie Dong
Publié dans: Journal of Dynamics and Differential Equations, 2020, ISSN 1040-7294
Éditeur: Plenum Publishers
DOI: 10.1007/s10884-020-09842-7

Lagrangian formulation and a priori estimates for relativistic fluid flows with vacuum

Auteurs: Juhi Jang, Philippe G. LeFloch, Nader Masmoudi
Publié dans: Journal of Differential Equations, Numéro 260/6, 2016, Page(s) 5481-5509, ISSN 0022-0396
Éditeur: Academic Press
DOI: 10.1016/j.jde.2015.12.004

Gaussian wave packet transform based numerical scheme for the semi-classical Schrödinger equation with random inputs

Auteurs: Shi Jin, Liu Liu, Giovanni Russo, Zhennan Zhou
Publié dans: Journal of Computational Physics, Numéro 401, 2020, Page(s) 109015, ISSN 0021-9991
Éditeur: Academic Press
DOI: 10.1016/j.jcp.2019.109015

Mathematics of computational modelling: some challenges of computing nonlinear phenomena

Auteurs: I. Gkanis, G. Grekas, E. Karnessis & C. Makridakis
Publié dans: First Congress of Greek Mathematicians - Proceedings of the Congress held in Athens, Greece, June 25–30, 2018, 2020, Page(s) 139-166, ISBN 9783110663075
Éditeur: De Gruyter
DOI: 10.1515/9783110663075-007

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