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Extreme SIGNED

An Exascale aware and Un-crashable Space-Time-Adaptive Discontinuous Spectral Element Solver for Non-Linear Conservation Laws

Total Cost €


EC-Contrib. €






Project "Extreme" data sheet

The following table provides information about the project.


Organization address
city: KOELN
postcode: 50931

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Total cost 1˙495˙875 €
 EC max contribution 1˙495˙875 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-04-01   to  2022-03-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAET ZU KOELN DE (KOELN) coordinator 1˙495˙875.00


 Project objective

'The dynamics of fluids and plasma is described by non-linear conservation laws. Transient behaviour on multiple scales involving turbulence and shocks is intrinsic to these problems. Due to their low dispersion and dissipation errors, adaptive high order numerical methods currently receive growing attention in academia and industry and form an emerging key technology. The potential benefits are massively improved computational efficiency and drastic reduction in memory consumption. Both benefits can be easily justified theoretically, in particular for a space-time adaptive high order method. However, due to high algorithmic complexity, the theoretical performance is difficult to sustain on massively parallel supercomputers. The first challenge that we will address in this project is to design novel, exascale aware, space-time adaptive algorithms and implement them in an open source solver that will scale on over 10^6 computing cores. Another indispensable property for the successful industrialisation of space-time adaptive high order methods is robustness. Robustness, i.e. an 'un-crashable' solver, which still retains all the positive benefits of the high order scheme is the 'holy grail' of the current research on these methods. This requires new mathematical concepts. The second challenge we will address here is to construct a provable un-crashable, space-time adaptive, high order solver without excessive artificial dissipation. Our mathematical key to achieve robustness is not intuitive at first sight: skew-symmetry. We will show that a specific skew-symmetric formulation guided by careful mathematics will allow us to design methods that are consistent with the second law of thermodynamics. This physical consistency is important as it will enable us to construct a new class of un-crashable space-time adaptive high order methods. We will demonstrate the supremacy of this efficient and robust solver in complex large scale science and engineering applications.'


year authors and title journal last update
List of publications.
2019 Andrew R. Winters,Christof Czernik,Moritz B. Schily,Gregor J. Gassner
Entropy stable numerical approximations for the isothermal and polytropic Euler equations
published pages: , ISSN: 1572-9125, DOI: 10.1007/s10543-019-00789-w
BIT Numerical Mathematics 2020-02-04
2019 David A. Kopriva, Florian J. Hindenlang, Thomas Bolemann, Gregor J. Gassner
Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements
published pages: 1389-1408, ISSN: 0885-7474, DOI: 10.1007/s10915-018-00897-9
Journal of Scientific Computing 79/3 2020-02-04
2019 Philipp Birken, Gregor J. Gassner, Lea M. Versbach
Subcell finite volume multigrid preconditioning for high-order discontinuous Galerkin methods
published pages: 353-361, ISSN: 1061-8562, DOI: 10.1080/10618562.2019.1667983
International Journal of Computational Fluid Dynamics 33/9 2020-02-04
2018 Gregor J. Gassner, Andrew R. Winters, Florian J. Hindenlang, David A. Kopriva
The BR1 Scheme is Stable for the Compressible Navier–Stokes Equations
published pages: 154-200, ISSN: 0885-7474, DOI: 10.1007/s10915-018-0702-1
Journal of Scientific Computing 77/1 2020-02-04
2018 Dominik Derigs, Gregor J. Gassner, Stefanie Walch, Andrew R. Winters
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
published pages: 153-219, ISSN: 0012-0456, DOI: 10.1365/s13291-018-0178-9
Jahresbericht der Deutschen Mathematiker-Vereinigung 120/3 2020-02-04
2019 Lucas Friedrich, Gero Schnücke, Andrew R. Winters, David C. Del Rey Fernández, Gregor J. Gassner, Mark H. Carpenter
Entropy Stable Space–Time Discontinuous Galerkin Schemes with Summation-by-Parts Property for Hyperbolic Conservation Laws
published pages: 175-222, ISSN: 0885-7474, DOI: 10.1007/s10915-019-00933-2
Journal of Scientific Computing 80/1 2020-02-04
2018 Niklas Wintermeyer, Andrew R. Winters, Gregor J. Gassner, Timothy Warburton
An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs
published pages: 447-480, ISSN: 0021-9991, DOI: 10.1016/
Journal of Computational Physics 375 2019-07-18
2017 David Flad, Gregor Gassner
On the use of kinetic energy preserving DG-schemes for large eddy simulation
published pages: 782-795, ISSN: 0021-9991, DOI: 10.1016/
Journal of Computational Physics 350 2019-07-18
2018 Marvin Bohm, Andrew R. Winters, Gregor J. Gassner, Dominik Derigs, Florian Hindenlang, Joachim Saur
An entropy stable nodal discontinuous Galerkin method for the resistive MHD equations. Part I: Theory and numerical verification
published pages: , ISSN: 0021-9991, DOI: 10.1016/
Journal of Computational Physics 2019-07-18
2018 Andrew R. Winters, Rodrigo C. Moura, Gianmarco Mengaldo, Gregor J. Gassner, Stefanie Walch, Joaquim Peiro, Spencer J. Sherwin
A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations
published pages: 1-21, ISSN: 0021-9991, DOI: 10.1016/
Journal of Computational Physics 372 2019-07-18
2018 Dominik Derigs, Andrew R. Winters, Gregor J. Gassner, Stefanie Walch, Marvin Bohm
Ideal GLM-MHD: About the entropy consistent nine-wave magnetic field divergence diminishing ideal magnetohydrodynamics equations
published pages: 420-467, ISSN: 0021-9991, DOI: 10.1016/
Journal of Computational Physics 364 2019-07-18
2018 Gregor J. Gassner, Andrew R. Winters, Florian J. Hindenlang, David A. Kopriva
Correction to: The BR1 Scheme is Stable for the Compressible Navier–Stokes Equations
published pages: 201-203, ISSN: 0885-7474, DOI: 10.1007/s10915-018-0758-y
Journal of Scientific Computing 77/1 2019-07-18

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