Modelling and Computation of Shocks and Interfaces

Deliverables

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

Author(s): Georgios Grekas, Maria Proestaki, Phoebus Rosakis, Jacob Notbohm, Charalambos Makridakis, Guruswami Ravichandran
Published in: Journal of The Royal Society Interface, Issue 18/175, 2021, ISSN 1742-5662
Publisher: The Royal Society
DOI: 10.1098/rsif.2020.0823

Flow solutions of transport equations

Author(s): Sholeh Karimghasemi, Siegfried Müller, Michael Westdickenberg
Published in: Communications in Partial Differential Equations, Issue 46/1, 2021, Page(s) 98-134, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2020.1831018

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

Author(s): Adrian M. Ruf, Espen Sande, Susanne Solem
Published in: Journal of Scientific Computing, Issue 80/3, 2019, Page(s) 1764-1776, ISSN 0885-7474
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-00996-1

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

Author(s): Rémi Abgrall, Davide Torlo
Published in: SIAM Journal on Scientific Computing, Issue 42/3, 2020, Page(s) B816-B845, ISSN 1064-8275
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m128973x

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

Author(s): Neelabja Chatterjee, Ulrik Skre Fjordholm
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 54/4, 2020, Page(s) 1415-1428, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2019090

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

Author(s): Nils Henrik Risebro, Adrian M. Ruf
Published in: SeMA Journal, Issue 77/2, 2020, Page(s) 143-159, ISSN 2254-3902
Publisher: Springer
DOI: 10.1007/s40324-019-00207-9

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

Author(s): Roberto Alicandro, Gianni Dal Maso, Giuliano Lazzaroni, Mariapia Palombaro
Published in: Archive for Rational Mechanics and Analysis, Issue 230/1, 2018, Page(s) 1-45, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-018-1240-6

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

Author(s): Ioannis Gkanis, Charalambos G. Makridakis
Published in: Mathematics of Computation, 2021, Page(s) 1, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3617

Models for Dense Multilane Vehicular Traffic

Author(s): Helge Holden, Nils Henrik Risebro
Published in: SIAM Journal on Mathematical Analysis, Issue 51/5, 2019, Page(s) 3694-3713, ISSN 0036-1410
Publisher: 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

Author(s): Jan Giesselmann, Philippe G. LeFloch
Published in: Numerische Mathematik, Issue 144/4, 2020, Page(s) 751-785, ISSN 0029-599X
Publisher: Springer Verlag
DOI: 10.1007/s00211-020-01101-7

The inverse-deformation approach to fracture

Author(s): Phoebus Rosakis, Timothy J. Healey, Uğur Alyanak
Published in: Journal of the Mechanics and Physics of Solids, Issue 150, 2021, Page(s) 104352, ISSN 0022-5096
Publisher: 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

Author(s): François Bouchut, Christophe Chalons, Sébastien Guisset
Published in: Numerische Mathematik, Issue 145/1, 2020, Page(s) 35-76, ISSN 0029-599X
Publisher: 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

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

Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

Author(s): Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Published in: Discrete & Continuous Dynamical Systems - A, Issue 39/11, 2019, Page(s) 6175-6206, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019269

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

Author(s): H. Carrillo, C. Parés, D. Zorío
Published in: Journal of Scientific Computing, Issue 86/1, 2021, ISSN 0885-7474
Publisher: 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

Author(s): Yangyang Cao
Published in: Communications in Computational Physics, Issue 29/2, 2020, Page(s) 472-509, ISSN 1815-2406
Publisher: Global Science Press
DOI: 10.4208/cicp.oa-2020-0033

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

Author(s): Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Published in: Annales Henri Poincaré, 2020, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-020-00955-9

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

Author(s): Elena Gaburro; Manuel J. Castro; Michael Dumbser
Published in: Science Direct, Issue Volume 175, 15 October 2018, 2018, Page(s) Pages 180 - 198, ISSN 0045-7930
Publisher: 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

Author(s): Francesco De Anna, Arghir Zarnescu
Published in: Journal of Differential Equations, Issue 264/2, 2018, Page(s) 1080-1118, ISSN 0022-0396
Publisher: 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

Author(s): A. M. Ruf
Published in: Zeitschrift für angewandte Mathematik und Physik, Issue 68/5, 2017, ISSN 0044-2275
Publisher: 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

Author(s): Elena Gaburro, Manuel J Castro, Michael Dumbser
Published in: Monthly Notices of the Royal Astronomical Society, Issue 477/2, 2018, Page(s) 2251-2275, ISSN 0035-8711
Publisher: Blackwell Publishing Inc.
DOI: 10.1093/mnras/sty542

Convergence of the finite volume method on a Schwarzschild background

Author(s): Shijie Dong, Philippe G. LeFloch
Published in: ESAIM: Mathematical Modelling and Numerical Analysis, Issue 53/5, 2019, Page(s) 1459-1476, ISSN 0764-583X
Publisher: EDP Sciences
DOI: 10.1051/m2an/2019037

Compact Approximate Taylor Methods for Systems of Conservation Laws

Author(s): H. Carrillo, C. Parés
Published in: Journal of Scientific Computing, Issue 80/3, 2019, Page(s) 1832-1866, ISSN 0885-7474
Publisher: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-01005-1

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

Author(s): Stavros Avgerinos, Florian Bernard, Angelo Iollo, Giovanni Russo
Published in: Journal of Computational Physics, Issue 393, 2019, Page(s) 278-312, ISSN 0021-9991
Publisher: 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

Author(s): G. M. Coclite, N. Chatterjee, N. H. Risebro
Published in: Milan Journal of Mathematics, Issue 87/2, 2019, Page(s) 283-301, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-019-00302-6

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

Author(s): Shijie Dong, Zoe Wyatt
Published in: Journal of Differential Equations, Issue 269/9, 2020, Page(s) 7470-7497, ISSN 0022-0396
Publisher: Academic Press
DOI: 10.1016/j.jde.2020.05.019

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

Author(s): Elena Gaburro, Michael Dumbser, Manuel J. Castro
Published in: Computers & Fluids, Issue 169, 2018, Page(s) 263-284, ISSN 0045-7930
Publisher: 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

Author(s): Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Published in: Communications in Partial Differential Equations, Issue 43/7, 2018, Page(s) 1019-1050, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2018.1456551

Weak solution of the merged mathematical equations of the polluted atmosphere

Author(s): Donatella Donatelli, Nóra Juhász
Published in: Mathematical Methods in the Applied Sciences, Issue 43/15, 2020, Page(s) 9245-9261, ISSN 0170-4214
Publisher: 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

Author(s): Donatella Donatelli, Tessa Thorsen, Konstantina Trivisa
Published in: Kinetic & Related Models, Issue 13/5, 2020, Page(s) 1047-1070, ISSN 1937-5077
Publisher: 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

Author(s): S. Boscarino, G. Russo, L. Scandurra
Published in: Journal of Scientific Computing, Issue 77/2, 2018, Page(s) 850-884, ISSN 0885-7474
Publisher: 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

Author(s): Johanna Ridder, Adrian Montgomery Ruf
Published in: BIT Numerical Mathematics, Issue 59, (2019), 2019, Page(s) pages775–796, ISSN 0006-3835
Publisher: Springer
DOI: 10.1007/s10543-019-00746-7

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

Author(s): N Chatterjee, U S Fjordholm
Published in: IMA Journal of Numerical Analysis, Issue 40/1, 2018, Page(s) 405-421, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/dry074

Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux

Author(s): Jayesh Badwaik, Adrian M. Ruf
Published in: SIAM Journal on Numerical Analysis, Issue 58/1, 2020, Page(s) 607-629, ISSN 0036-1429
Publisher: 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

Author(s): Donatella Donatelli, Konstantina Trivisa
Published in: Journal of Mathematical Analysis and Applications, Issue 482/1, 2020, Page(s) 123527, ISSN 0022-247X
Publisher: Academic Press
DOI: 10.1016/j.jmaa.2019.123527

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

Author(s): Shijie Dong
Published in: Journal of Dynamics and Differential Equations, 2020, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-020-09842-7

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

Author(s): Juhi Jang, Philippe G. LeFloch, Nader Masmoudi
Published in: Journal of Differential Equations, Issue 260/6, 2016, Page(s) 5481-5509, ISSN 0022-0396
Publisher: 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

Author(s): Shi Jin, Liu Liu, Giovanni Russo, Zhennan Zhou
Published in: Journal of Computational Physics, Issue 401, 2020, Page(s) 109015, ISSN 0021-9991
Publisher: Academic Press
DOI: 10.1016/j.jcp.2019.109015

Mathematics of computational modelling: some challenges of computing nonlinear phenomena

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

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