## HE-E1GODF

 swMATH ID: 6606 Software Authors: Toro, E. F Description: Riemann solver to solve the time-dependent one dimensional Euler equations for an ideal gas by Godunov methods with several approximate Rieman solvers of the approximate flux type: Roe Riemann solver, HLLC Riemann solver, HLL Riemann solver, Rusanov ”Riemann” solver Code: HE-E1GODF.F Homepage: https://math.nyu.edu/~jbu200/E1GODF.F Programming Languages: FORTRAN Keywords: Riemann solver; Roe; Rusanov; Godunov methods; HLL; HLLC Related Software: HLLE; AUSM; MOOD; SHASTA; ReALE; RODAS; HLLC; Gmsh; FLASH; RIEMANN; Spalart-Allmaras; Athena; CLAWPACK; deal.ii; SLIC; GFORCE; PETSc; CUDA; ADER-DG; SWASHES Cited in: 989 Publications
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### Cited by 1,689 Authors

 29 Toro, Eleuterio Francisco 26 Dumbser, Michael 21 Berthon, Christophe 20 Boscheri, Walter 17 Liu, Tiegang 16 Saurel, Richard 15 Adams, Nikolaus A. 15 Vázquez-Cendón, María Elena 15 Xiao, Feng 13 Li, Jiequan 13 Munz, Claus-Dieter 12 Kurganov, Alexander 11 Shu, Chi-Wang 10 Xu, Kun 9 Deng, Xi 9 Gavrilyuk, Sergey L. 9 Khoo, Boo Cheong 9 Loubère, Raphaël 9 Titarev, Vladimir A. 8 Chandrashekar, Praveen 8 Guermond, Jean-Luc 8 Klingenberg, Christian 8 Murillo, Javier 8 Popov, Boyan 7 Dimarco, Giacomo 7 Favrie, Nicolas 7 Foucher, Françoise 7 Garcia-Navarro, Pilar 7 Gassner, Gregor J. 7 Kopriva, David Alan 7 Winters, Andrew R. 6 Bermúdez, Alfredo 6 Bouchut, François 6 Busto, Saray 6 Chiapolino, Alexandre 6 Clain, Stéphane Louis 6 Després, Bruno 6 Drikakis, Dimitris 6 Dubey, Ritesh Kumar 6 Lee, Dongwook 6 Montecinos, Gino I. 6 Navas-Montilla, A. 6 Parés Madroñal, Carlos 6 Tang, Huazhong 6 Turpault, Rodolphe 6 Valero, Eusebio 6 Xie, Bin 5 Abgrall, Rémi 5 Borsche, Raul 5 Chalons, Christophe 5 Chertock, Alina E. 5 Colominas, Ignasi 5 Colonius, Tim 5 Ferrer, Esteban 5 Glaubitz, Jan 5 Iollo, Angelo 5 Kumar, Rakesh 5 Liu, Qinghuo 5 Michel-Dansac, Victor 5 Müller, Lucas Omar 5 Müller, Siegfried 5 Nguyen, Van-Tu 5 Nogueira, Xesús 5 Park, Warn-Gyu 5 Rubio, Gonzalo 5 Saavedra, Laura 5 Shashkov, Mikhail J. 5 Shyue, Keh-Ming 5 Xiong, Tao 5 Zeidan, Dia 5 Zhan, Qiwei 5 Zhang, Qinglong 5 Zhuang, Mingwei 4 Adami, Stefan 4 Barsukow, Wasilij 4 Bonet, Javier 4 Cheng, Jian 4 Daude, Frédéric 4 Dong, Haitao 4 Dubroca, Bruno 4 Galon, Pascal 4 Gil, Antonio J. 4 Gray, John Mark Nicholas Timm 4 Guillard, Hervé 4 Hidalgo, Arturo 4 Käppeli, Roger 4 Klein, Rupert 4 Kumar, Harish 4 Kuzmin, Dmitri 4 Lee, Chun Hean 4 Liang, Qiuhua 4 Liu, Fujun 4 López, Xián 4 Nikiforakis, Nikos 4 Nkonga, Boniface 4 Öffner, Philipp 4 Pudjaprasetya, Sri Redjeki 4 Qiu, Jianxian 4 Raghurama Rao, S. V. 4 Russo, Giovanni ...and 1,589 more Authors
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### Cited in 130 Serials

 344 Journal of Computational Physics 124 Computers and Fluids 69 Journal of Scientific Computing 44 Computer Methods in Applied Mechanics and Engineering 26 Applied Mathematics and Computation 23 International Journal for Numerical Methods in Fluids 22 SIAM Journal on Scientific Computing 16 Computers & Mathematics with Applications 15 International Journal of Computational Fluid Dynamics 14 Communications in Computational Physics 12 Journal of Fluid Mechanics 12 Applied Numerical Mathematics 9 Numerische Mathematik 8 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 7 Computer Physics Communications 7 Wave Motion 7 Mathematics of Computation 7 International Journal for Numerical Methods in Engineering 7 Computational Geosciences 7 Matematicheskoe Modelirovanie 6 Applied Mathematical Modelling 5 Journal of Computational and Applied Mathematics 5 Computational Mathematics and Mathematical Physics 4 Classical and Quantum Gravity 4 SIAM Journal on Numerical Analysis 4 SIAM Journal on Mathematical Analysis 4 Archives of Computational Methods in Engineering 4 International Journal on Finite Volumes 3 Journal of Engineering Mathematics 3 Journal of Mathematical Biology 3 Shock Waves 3 BIT 3 Mathematics and Computers in Simulation 3 Quarterly of Applied Mathematics 3 Numerical Methods for Partial Differential Equations 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Computational and Applied Mathematics 3 Engineering Analysis with Boundary Elements 3 Mathematical Problems in Engineering 3 European Journal of Mechanics. B. Fluids 3 Journal of Hyperbolic Differential Equations 3 International Journal of Numerical Analysis and Modeling 3 Kinetic and Related Models 3 Advances in Applied Mathematics and Mechanics 2 Acta Mechanica 2 IMA Journal of Numerical Analysis 2 Nonlinearity 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Applied Mathematics Letters 2 Numerical Algorithms 2 Physics of Fluids 2 Electronic Journal of Differential Equations (EJDE) 2 Russian Journal of Numerical Analysis and Mathematical Modelling 2 Differential Equations and Dynamical Systems 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Communications in Nonlinear Science and Numerical Simulation 2 Living Reviews in Relativity 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Communications in Mathematical Sciences 2 Networks and Heterogeneous Media 2 International Journal of Advances in Engineering Sciences and Applied Mathematics 2 East Asian Journal on Applied Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings and Surveys 2 Communications on Applied Mathematics and Computation 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Astronomy and Astrophysics 1 Astrophysics and Space Science 1 International Journal of Heat and Mass Transfer 1 Indian Journal of Pure & Applied Mathematics 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Mathematical Physics 1 Mathematical Methods in the Applied Sciences 1 Russian Mathematical Surveys 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Calcolo 1 Meccanica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Acta Applicandae Mathematicae 1 Journal of Economic Dynamics & Control 1 Mathematical and Computer Modelling 1 Journal of Non-Equilibrium Thermodynamics 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 International Journal of Modern Physics D 1 International Journal of Numerical Methods for Heat & Fluid Flow 1 Methods and Applications of Analysis 1 Advances in Computational Mathematics 1 Journal of Mathematical Chemistry 1 Computing and Visualization in Science 1 Vietnam Journal of Mathematics 1 Abstract and Applied Analysis 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Far East Journal of Applied Mathematics 1 Mathematical and Computer Modelling of Dynamical Systems 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences ...and 30 more Serials
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### Cited in 33 Fields

 767 Fluid mechanics (76-XX) 577 Numerical analysis (65-XX) 339 Partial differential equations (35-XX) 65 Mechanics of deformable solids (74-XX) 40 Geophysics (86-XX) 36 Classical thermodynamics, heat transfer (80-XX) 25 Statistical mechanics, structure of matter (82-XX) 24 Astronomy and astrophysics (85-XX) 18 Biology and other natural sciences (92-XX) 14 Optics, electromagnetic theory (78-XX) 11 Operations research, mathematical programming (90-XX) 10 Relativity and gravitational theory (83-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 Computer science (68-XX) 4 Approximations and expansions (41-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Probability theory and stochastic processes (60-XX) 3 Mechanics of particles and systems (70-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Statistics (62-XX) 1 Quantum theory (81-XX) 1 Systems theory; control (93-XX) 1 Mathematics education (97-XX)