swMATH ID: 6605
Software Authors: Harten, Amiram; Lax, Peter D.; van Leer, Bram
Description: The HLLE[3] (Harten, Lax, van Leer and Einfeldt) solver is an approximate solution to the Riemann problem, which is only based on the integral form of the conservation laws and the largest and smallest signal velocities at the interface. The stability and robustness of the HLLE solver is closely related to the signal velocities and a single central average state, as proposed by Einfeldt in the original paper. The description of the HLLE scheme in the book mentioned below is incomplete and partially wrong. The reader is referred to the original paper. Actually, the HLLE scheme is based on a new stability theory for discontinuities in fluids, which was never published. HLLC solver The HLLC (Harten-Lax-van Leer-Contact) solver was introduced by Toro.[4] It restores the missing Rarefaction wave by some estimates, like linearisations, these can be simple but also more advanced exists like using the Roe average velocity for the middle wave speed. They are quite robust and efficient but somewhat more diffusive.[5]
https://math.nyu.edu/ jbu200/E1GODF.F
Homepage: http://en.wikipedia.org/wiki/Riemann_solver#HLLE_solver
Keywords: Riemann solver
Cited in: 718 Publications
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Cited by 1,176 Authors

30 Berthon, Christophe
19 Dumbser, Michael
15 Toro, Eleuterio Francisco
14 Balsara, Dinshaw S.
14 Chalons, Christophe
14 Saurel, Richard
11 Turpault, Rodolphe
10 Parés Madroñal, Carlos
9 Kurganov, Alexander
9 Nkonga, Boniface
9 Shu, Chi-Wang
8 Castro, Manuel J.
8 Coquel, Frédéric
7 Capdeville, Guy
7 Dubroca, Bruno
7 Foucher, Françoise
7 Liu, Tiegang
6 Bouchut, François
6 Chen, Shusheng
6 Titarev, Vladimir A.
6 van Leer, Bram
6 Yan, Chao
5 Abgrall, Rémi
5 Adams, Nikolaus A.
5 Boscheri, Walter
5 Clain, Stéphane Louis
5 Cueto-Felgueroso, Luis
5 Godlewski, Edwige
5 Groth, Clinton P. T.
5 Guinot, Vincent
5 Harten, Ami
5 Helluy, Philippe
5 Hérard, Jean-Marc
5 Hu, Lijun
5 Kapen, Pascalin Tiam
5 Khoo, Boo Cheong
5 Kitamura, Keiichi
5 Mandal, Jadav Chandra
5 McDonald, James G.
5 Munz, Claus-Dieter
5 Seguin, Nicolas
5 Shen, Zhijun
5 Shyue, Keh-Ming
5 Tian, Zhengyu
5 Vázquez-Cendón, María Elena
5 Xiao, Feng
5 Xie, Wenfeng
5 Xu, Kun
4 Audit, Edouard
4 Castro-Díaz, Manuel Jesús
4 Causon, D. M.
4 Chandrashekar, Praveen
4 Chiapolino, Alexandre
4 Colominas, Ignasi
4 Dawson, Clint N.
4 Drikakis, Dimitris
4 Fernández-Nieto, Enrique Domingo
4 Font, José A.
4 Frank, Martin
4 Guisset, Sebastien
4 Ingram, David M.
4 Johnsen, Eric
4 Klingenberg, Christian
4 Klingenberg, Christian F.
4 Kulikov, Igor M.
4 Kusch, Jonas
4 Le, Minh Hoang
4 LeFloch, Philippe Gerard
4 Liu, Kai
4 Mathis, Hélène
4 Michel-Dansac, Victor
4 Morales de Luna, Tomás
4 Navarrina, Fermín
4 Pelanti, Marica
4 Perthame, Benoît
4 Puertas, Jerónimo
4 Qamar, Shamsul
4 Raghurama Rao, S. V.
4 Raviart, Pierre-Arnaud
4 Renac, Florent
4 Rosatti, Giorgio
4 San, Omer
4 Waagan, Knut
4 Wendroff, Burton
4 Xie, Wenjia
3 Adami, Stefan
3 Bermúdez, Alfredo
3 Blachère, Florian
3 Brull, Stephane
3 Cai, Zhenning
3 Cancès, Clément
3 Celledoni, Elena
3 Chakravarthy, Sukumar R.
3 Chertock, Alina E.
3 Daude, Frédéric
3 Davis, Stephen F.
3 De Vuyst, Florian
3 Deng, Xi
3 Dong, Jian
3 Duran, Arnaud
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Cited in 101 Serials

241 Journal of Computational Physics
90 Computers and Fluids
28 Journal of Scientific Computing
21 Computer Methods in Applied Mechanics and Engineering
17 SIAM Journal on Scientific Computing
16 International Journal for Numerical Methods in Fluids
14 Communications in Computational Physics
13 Computers & Mathematics with Applications
13 Journal of Fluid Mechanics
13 Applied Numerical Mathematics
12 Mathematics of Computation
12 Applied Mathematics and Computation
12 Journal of Computational and Applied Mathematics
11 SIAM Journal on Numerical Analysis
11 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
8 Numerische Mathematik
8 International Journal of Computational Fluid Dynamics
7 Shock Waves
7 Applied Mathematical Modelling
6 International Journal on Finite Volumes
5 Numerical Methods for Partial Differential Equations
5 Computational Mathematics and Mathematical Physics
5 European Journal of Mechanics. B. Fluids
5 Archives of Computational Methods in Engineering
4 Classical and Quantum Gravity
4 International Journal for Numerical Methods in Engineering
4 Computational Mechanics
4 Continuum Mechanics and Thermodynamics
4 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
4 Communications in Nonlinear Science and Numerical Simulation
4 Advances in Applied Mathematics and Mechanics
4 SMAI Journal of Computational Mathematics
3 Computational Mathematics and Modeling
3 Advances in Computational Mathematics
3 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings
3 Living Reviews in Relativity
2 Computer Physics Communications
2 ZAMP. Zeitschrift für angewandte Mathematik und Physik
2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki
2 Calcolo
2 Mathematics and Computers in Simulation
2 SIAM Journal on Scientific and Statistical Computing
2 Applied Mathematics Letters
2 Communications in Numerical Methods in Engineering
2 Mathematical Problems in Engineering
2 Computational Geosciences
2 Lobachevskii Journal of Mathematics
2 Communications in Mathematical Sciences
2 Applied Mathematical Sciences
2 Networks and Heterogeneous Media
2 SIAM/ASA Journal on Uncertainty Quantification
2 International Journal of Applied and Computational Mathematics
2 Communications on Applied Mathematics and Computation
1 Communications on Pure and Applied Mathematics
1 Journal of Engineering Mathematics
1 Journal of Statistical Physics
1 Mathematical Methods in the Applied Sciences
1 Nonlinearity
1 Bulletin of the Polish Academy of Sciences. Technical Sciences
1 Kybernetika
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Transactions of the American Mathematical Society
1 Journal of Computational Mathematics
1 Acta Mathematicae Applicatae Sinica. English Series
1 Mathematical and Computer Modelling
1 Japan Journal of Industrial and Applied Mathematics
1 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
1 Numerical Algorithms
1 SIAM Review
1 Mémoires de la Société Mathématique de France. Nouvelle Série
1 Philosophical Transactions of the Royal Society of London. Series A
1 Journal of Nonlinear Science
1 Computational Optimization and Applications
1 Physics of Fluids
1 Annales Mathématiques Blaise Pascal
1 International Journal of Numerical Methods for Heat & Fluid Flow
1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences
1 Flow, Turbulence and Combustion
1 Nonlinear Analysis. Real World Applications
1 Matematicheskoe Modelirovanie
1 Journal of Applied Mathematics
1 Communications in Information and Systems
1 Bulletin of the Brazilian Mathematical Society. New Series
1 Multiscale Modeling & Simulation
1 Acta Numerica
1 Springer Series in Computational Mathematics
1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A1. Informatica
1 International Journal of Mathematical Analysis (Ruse)
1 SIAM Journal on Imaging Sciences
1 Kinetic and Related Models
1 Numerical Mathematics: Theory, Methods and Applications
1 Confluentes Mathematici
1 GEM - International Journal on Geomathematics
1 International Journal of Advances in Engineering Sciences and Applied Mathematics
1 S\(\vec{\text{e}}\)MA Journal
1 Journal of Computational Methods in Physics
1 AMM. Applied Mathematics and Mechanics. (English Edition)
1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys
1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
1 Frontiers in Mathematics
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