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Low complexity shape optimization & a posteriori high fidelity validation
A robust wellbalanced scheme for multilayer shallow water equations
1.  DMA, CNRS & École Normale Supérieure, 45 Rue d’Ulm, F75230 Paris cedex 05, France 
2.  LMD, École Normale Supérieure, 24 Rue Lhomond, F75231 Paris cedex 05, France 
[1] 
Nora Aïssiouene, MarieOdile Bristeau, Edwige Godlewski, Jacques SainteMarie. A combined finite volume  finite element scheme for a dispersive shallow water system. Networks & Heterogeneous Media, 2016, 11 (1) : 127. doi: 10.3934/nhm.2016.11.1 
[2] 
Qingshan Chen. On the wellposedness of the inviscid multilayer quasigeostrophic equations. Discrete & Continuous Dynamical Systems  A, 2019, 39 (6) : 32153237. doi: 10.3934/dcds.2019133 
[3] 
Andreas Hiltebrand, Siddhartha Mishra. Entropy stability and wellbalancedness of spacetime DG for the shallow water equations with bottom topography. Networks & Heterogeneous Media, 2016, 11 (1) : 145162. doi: 10.3934/nhm.2016.11.145 
[4] 
T. Tachim Medjo. Multilayer quasigeostrophic equations of the ocean with delays. Discrete & Continuous Dynamical Systems  B, 2008, 10 (1) : 171196. doi: 10.3934/dcdsb.2008.10.171 
[5] 
MarieOdile Bristeau, Jacques SainteMarie. Derivation of a nonhydrostatic shallow water model; Comparison with SaintVenant and Boussinesq systems. Discrete & Continuous Dynamical Systems  B, 2008, 10 (4) : 733759. doi: 10.3934/dcdsb.2008.10.733 
[6] 
Boris Andreianov, Nicolas Seguin. Analysis of a Burgers equation with singular resonant source term and convergence of wellbalanced schemes. Discrete & Continuous Dynamical Systems  A, 2012, 32 (6) : 19391964. doi: 10.3934/dcds.2012.32.1939 
[7] 
Laurent Gosse. Wellbalanced schemes using elementary solutions for linear models of the Boltzmann equation in one space dimension. Kinetic & Related Models, 2012, 5 (2) : 283323. doi: 10.3934/krm.2012.5.283 
[8] 
Ronald E. Mickens. A nonstandard finite difference scheme for the driftdiffusion system. Conference Publications, 2009, 2009 (Special) : 558563. doi: 10.3934/proc.2009.2009.558 
[9] 
Madalina Petcu, Roger Temam. An interface problem: The twolayer shallow water equations. Discrete & Continuous Dynamical Systems  A, 2013, 33 (11&12) : 53275345. doi: 10.3934/dcds.2013.33.5327 
[10] 
Justin Cyr, Phuong Nguyen, Roger Temam. Stochastic one layer shallow water equations with Lévy noise. Discrete & Continuous Dynamical Systems  B, 2019, 24 (8) : 37653818. doi: 10.3934/dcdsb.2018331 
[11] 
JeanFrédéric Gerbeau, Benoit Perthame. Derivation of viscous SaintVenant system for laminar shallow water; Numerical validation. Discrete & Continuous Dynamical Systems  B, 2001, 1 (1) : 89102. doi: 10.3934/dcdsb.2001.1.89 
[12] 
Marta Strani. Existence and uniqueness of a positive connection for the scalar viscous shallow water system in a bounded interval. Communications on Pure & Applied Analysis, 2014, 13 (4) : 16531667. doi: 10.3934/cpaa.2014.13.1653 
[13] 
Huijun He, Zhaoyang Yin. On the Cauchy problem for a generalized twocomponent shallow water wave system with fractional higherorder inertia operators. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 15091537. doi: 10.3934/dcds.2017062 
[14] 
Djano Kandaswamy, Thierry Blu, Dimitri Van De Ville. Analytic sensing for multilayer spherical models with application to EEG source imaging. Inverse Problems & Imaging, 2013, 7 (4) : 12511270. doi: 10.3934/ipi.2013.7.1251 
[15] 
Fujun Zhou, Junde Wu, Shangbin Cui. Existence and asymptotic behavior of solutions to a moving boundary problem modeling the growth of multilayer tumors. Communications on Pure & Applied Analysis, 2009, 8 (5) : 16691688. doi: 10.3934/cpaa.2009.8.1669 
[16] 
T. Tachim Medjo. Averaging of a multilayer quasigeostrophic equations with oscillating external forces. Communications on Pure & Applied Analysis, 2014, 13 (3) : 11191140. doi: 10.3934/cpaa.2014.13.1119 
[17] 
Johannes Eilinghoff, Roland Schnaubelt. Error analysis of an ADI splitting scheme for the inhomogeneous Maxwell equations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (11) : 56855709. doi: 10.3934/dcds.2018248 
[18] 
Manh Hong Duong, Yulong Lu. An operator splitting scheme for the fractional kinetic FokkerPlanck equation. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 57075727. doi: 10.3934/dcds.2019250 
[19] 
Florian Schneider, Jochen Kall, Graham Alldredge. A realizabilitypreserving highorder kinetic scheme using WENO reconstruction for entropybased moment closures of linear kinetic equations in slab geometry. Kinetic & Related Models, 2016, 9 (1) : 193215. doi: 10.3934/krm.2016.9.193 
[20] 
Zhaoyang Yin. Wellposedness, blowup, and global existence for an integrable shallow water equation. Discrete & Continuous Dynamical Systems  A, 2004, 11 (2&3) : 393411. doi: 10.3934/dcds.2004.11.393 
2018 Impact Factor: 1.008
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