Modelling and Computation of Shocks and Interfaces

Resultado final

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

Publicaciones

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

Autores: Georgios Grekas, Maria Proestaki, Phoebus Rosakis, Jacob Notbohm, Charalambos Makridakis, Guruswami Ravichandran
Publicado en: Journal of The Royal Society Interface, Edición 18/175, 2021, ISSN 1742-5662
Editor: The Royal Society
DOI: 10.1098/rsif.2020.0823

Flow solutions of transport equations

Autores: Sholeh Karimghasemi, Siegfried Müller, Michael Westdickenberg
Publicado en: Communications in Partial Differential Equations, Edición 46/1, 2021, Página(s) 98-134, ISSN 0360-5302
Editor: Marcel Dekker Inc.
DOI: 10.1080/03605302.2020.1831018

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

Autores: Adrian M. Ruf, Espen Sande, Susanne Solem
Publicado en: Journal of Scientific Computing, Edición 80/3, 2019, Página(s) 1764-1776, ISSN 0885-7474
Editor: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-00996-1

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

Autores: Rémi Abgrall, Davide Torlo
Publicado en: SIAM Journal on Scientific Computing, Edición 42/3, 2020, Página(s) B816-B845, ISSN 1064-8275
Editor: Society for Industrial and Applied Mathematics
DOI: 10.1137/19m128973x

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

Autores: Neelabja Chatterjee, Ulrik Skre Fjordholm
Publicado en: ESAIM: Mathematical Modelling and Numerical Analysis, Edición 54/4, 2020, Página(s) 1415-1428, ISSN 0764-583X
Editor: EDP Sciences
DOI: 10.1051/m2an/2019090

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

Autores: Nils Henrik Risebro, Adrian M. Ruf
Publicado en: SeMA Journal, Edición 77/2, 2020, Página(s) 143-159, ISSN 2254-3902
Editor: Springer
DOI: 10.1007/s40324-019-00207-9

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

Autores: Roberto Alicandro, Gianni Dal Maso, Giuliano Lazzaroni, Mariapia Palombaro
Publicado en: Archive for Rational Mechanics and Analysis, Edición 230/1, 2018, Página(s) 1-45, ISSN 0003-9527
Editor: Springer Verlag
DOI: 10.1007/s00205-018-1240-6

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

Autores: Ioannis Gkanis, Charalambos G. Makridakis
Publicado en: Mathematics of Computation, 2021, Página(s) 1, ISSN 0025-5718
Editor: American Mathematical Society
DOI: 10.1090/mcom/3617

Models for Dense Multilane Vehicular Traffic

Autores: Helge Holden, Nils Henrik Risebro
Publicado en: SIAM Journal on Mathematical Analysis, Edición 51/5, 2019, Página(s) 3694-3713, ISSN 0036-1410
Editor: 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

Autores: Jan Giesselmann, Philippe G. LeFloch
Publicado en: Numerische Mathematik, Edición 144/4, 2020, Página(s) 751-785, ISSN 0029-599X
Editor: Springer Verlag
DOI: 10.1007/s00211-020-01101-7

The inverse-deformation approach to fracture

Autores: Phoebus Rosakis, Timothy J. Healey, Uğur Alyanak
Publicado en: Journal of the Mechanics and Physics of Solids, Edición 150, 2021, Página(s) 104352, ISSN 0022-5096
Editor: 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

Autores: François Bouchut, Christophe Chalons, Sébastien Guisset
Publicado en: Numerische Mathematik, Edición 145/1, 2020, Página(s) 35-76, ISSN 0029-599X
Editor: 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

Autores: J.C. González-Aguirre, M.J. Castro, T. Morales de Luna
Publicado en: Advances in Water Resources, Edición 140, 2020, Página(s) 103575, ISSN 0309-1708
Editor: Pergamon Press Ltd.
DOI: 10.1016/j.advwatres.2020.103575

Measure-valued solutions for the equations of polyconvex adiabatic thermoelasticity

Autores: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Publicado en: Discrete & Continuous Dynamical Systems - A, Edición 39/11, 2019, Página(s) 6175-6206, ISSN 1553-5231
Editor: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2019269

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

Autores: H. Carrillo, C. Parés, D. Zorío
Publicado en: Journal of Scientific Computing, Edición 86/1, 2021, ISSN 0885-7474
Editor: 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

Autores: Yangyang Cao
Publicado en: Communications in Computational Physics, Edición 29/2, 2020, Página(s) 472-509, ISSN 1815-2406
Editor: Global Science Press
DOI: 10.4208/cicp.oa-2020-0033

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

Autores: Shijie Dong, Philippe G. LeFloch, Zoe Wyatt
Publicado en: Annales Henri Poincaré, 2020, ISSN 1424-0637
Editor: Birkhauser Verlag
DOI: 10.1007/s00023-020-00955-9

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

Autores: Elena Gaburro; Manuel J. Castro; Michael Dumbser
Publicado en: Science Direct, Edición Volume 175, 15 October 2018, 2018, Página(s) Pages 180 - 198, ISSN 0045-7930
Editor: 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

Autores: Francesco De Anna, Arghir Zarnescu
Publicado en: Journal of Differential Equations, Edición 264/2, 2018, Página(s) 1080-1118, ISSN 0022-0396
Editor: 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

Autores: A. M. Ruf
Publicado en: Zeitschrift für angewandte Mathematik und Physik, Edición 68/5, 2017, ISSN 0044-2275
Editor: 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

Autores: Elena Gaburro, Manuel J Castro, Michael Dumbser
Publicado en: Monthly Notices of the Royal Astronomical Society, Edición 477/2, 2018, Página(s) 2251-2275, ISSN 0035-8711
Editor: Blackwell Publishing Inc.
DOI: 10.1093/mnras/sty542

Convergence of the finite volume method on a Schwarzschild background

Autores: Shijie Dong, Philippe G. LeFloch
Publicado en: ESAIM: Mathematical Modelling and Numerical Analysis, Edición 53/5, 2019, Página(s) 1459-1476, ISSN 0764-583X
Editor: EDP Sciences
DOI: 10.1051/m2an/2019037

Compact Approximate Taylor Methods for Systems of Conservation Laws

Autores: H. Carrillo, C. Parés
Publicado en: Journal of Scientific Computing, Edición 80/3, 2019, Página(s) 1832-1866, ISSN 0885-7474
Editor: Kluwer Academic/Plenum Publishers
DOI: 10.1007/s10915-019-01005-1

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

Autores: Stavros Avgerinos, Florian Bernard, Angelo Iollo, Giovanni Russo
Publicado en: Journal of Computational Physics, Edición 393, 2019, Página(s) 278-312, ISSN 0021-9991
Editor: 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

Autores: G. M. Coclite, N. Chatterjee, N. H. Risebro
Publicado en: Milan Journal of Mathematics, Edición 87/2, 2019, Página(s) 283-301, ISSN 1424-9286
Editor: Birkhauser Verlag
DOI: 10.1007/s00032-019-00302-6

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

Autores: Shijie Dong, Zoe Wyatt
Publicado en: Journal of Differential Equations, Edición 269/9, 2020, Página(s) 7470-7497, ISSN 0022-0396
Editor: Academic Press
DOI: 10.1016/j.jde.2020.05.019

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

Autores: Elena Gaburro, Michael Dumbser, Manuel J. Castro
Publicado en: Computers & Fluids, Edición 169, 2018, Página(s) 263-284, ISSN 0045-7930
Editor: 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

Autores: Cleopatra Christoforou, Myrto Galanopoulou, Athanasios E. Tzavaras
Publicado en: Communications in Partial Differential Equations, Edición 43/7, 2018, Página(s) 1019-1050, ISSN 0360-5302
Editor: Marcel Dekker Inc.
DOI: 10.1080/03605302.2018.1456551

Weak solution of the merged mathematical equations of the polluted atmosphere

Autores: Donatella Donatelli, Nóra Juhász
Publicado en: Mathematical Methods in the Applied Sciences, Edición 43/15, 2020, Página(s) 9245-9261, ISSN 0170-4214
Editor: 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

Autores: Donatella Donatelli, Tessa Thorsen, Konstantina Trivisa
Publicado en: Kinetic & Related Models, Edición 13/5, 2020, Página(s) 1047-1070, ISSN 1937-5077
Editor: 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

Autores: S. Boscarino, G. Russo, L. Scandurra
Publicado en: Journal of Scientific Computing, Edición 77/2, 2018, Página(s) 850-884, ISSN 0885-7474
Editor: 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

Autores: Johanna Ridder, Adrian Montgomery Ruf
Publicado en: BIT Numerical Mathematics, Edición 59, (2019), 2019, Página(s) pages775–796, ISSN 0006-3835
Editor: Springer
DOI: 10.1007/s10543-019-00746-7

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

Autores: N Chatterjee, U S Fjordholm
Publicado en: IMA Journal of Numerical Analysis, Edición 40/1, 2018, Página(s) 405-421, ISSN 0272-4979
Editor: Oxford University Press
DOI: 10.1093/imanum/dry074

Convergence Rates of Monotone Schemes for Conservation Laws with Discontinuous Flux

Autores: Jayesh Badwaik, Adrian M. Ruf
Publicado en: SIAM Journal on Numerical Analysis, Edición 58/1, 2020, Página(s) 607-629, ISSN 0036-1429
Editor: 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

Autores: Donatella Donatelli, Konstantina Trivisa
Publicado en: Journal of Mathematical Analysis and Applications, Edición 482/1, 2020, Página(s) 123527, ISSN 0022-247X
Editor: Academic Press
DOI: 10.1016/j.jmaa.2019.123527

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

Autores: Shijie Dong
Publicado en: Journal of Dynamics and Differential Equations, 2020, ISSN 1040-7294
Editor: Plenum Publishers
DOI: 10.1007/s10884-020-09842-7

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

Autores: Juhi Jang, Philippe G. LeFloch, Nader Masmoudi
Publicado en: Journal of Differential Equations, Edición 260/6, 2016, Página(s) 5481-5509, ISSN 0022-0396
Editor: 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

Autores: Shi Jin, Liu Liu, Giovanni Russo, Zhennan Zhou
Publicado en: Journal of Computational Physics, Edición 401, 2020, Página(s) 109015, ISSN 0021-9991
Editor: Academic Press
DOI: 10.1016/j.jcp.2019.109015

Mathematics of computational modelling: some challenges of computing nonlinear phenomena

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

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