| Issue |
ESAIM: M2AN
Volume 49, Number 3, May-June 2015
|
|
|---|---|---|
| Page(s) | 787 - 814 | |
| DOI | https://doi.org/10.1051/m2an/2014054 | |
| Published online | 08 April 2015 | |
Reduced basis techniques for nonlinear conservation laws
1 Department of Mechanical Engineering,
Massachusetts Institute of Technology, 77 Massachusetts Ave, Rm. 3-237
Cambridge, MA
02139,
USA.
ttaddei@mit.edu
2 MOX-Modeling and Scientific
Computing, Dipartimento di Matematica “F. Brioschi”, Politecnico di
Milano, Piazza Leonardo da Vinci
32, 20133
Milano, Italy.
simona.perotto@polimi.it; alfio.quarteroni@polimi.it
3 Modelling and Scientific Computing,
Institute of Analysis and Scientific Computing, École Polytechnique Féderale de
Lausanne, Station 8, EPFL, 1015
Lausanne,
Switzerland.
alfio.quarteroni@epfl.ch
Received:
10
August
2013
Revised:
29
September
2014
In this paper we present a new reduced basis technique for parametrized nonlinear scalar conservation laws in presence of shocks. The essential ingredients are an efficient algorithm to approximate the shock curve, a procedure to detect the smooth components of the solution at the two sides of the shock, and a suitable interpolation strategy to reconstruct such smooth components during the online stage. The approach we propose is based on some theoretical properties of the solution to the problem. Some numerical examples prove the effectiveness of the proposed strategy.
Mathematics Subject Classification: 65M08 / 65M15 / 65M25 / 35L65 / 35L67
Key words: Nonlinear conservation laws / model reduction / reduced basis method
© EDP Sciences, SMAI 2015
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