Аннотация:
Предложен новый класс квазилинейных гиперболических систем законов сохранения – подкласс систем уравнений, инвариантных относительно вращений. Каждая система из данного класса является термодинамически согласованной, т.е. имеет ряд дополнительных законов сохранения (один из которых в физических приложениях, как правило, является законом сохранения энергии или энтропии), а в записи уравнений используется только один производящий потенциал. Предложенный класс содержит большое число примеров уравнений механики сплошных сред в лагранжевых координатах.
Библиогр. 9.
Образец цитирования:
С. К. Годунов, Т. Ю. Михайлова, Е. И. Роменский, “Системы термодинамически согласованных законов сохранения, инвариантных относительно вращений”, Сиб. матем. журн., 37:4 (1996), 790–806; Siberian Math. J., 37:4 (1996), 690–705
Davide Ferrari, Ilya Peshkov, Evgeniy Romenski, Michael Dumbser, “A unified HTC multiphase model of continuum mechanics”, Journal of Computational Physics, 521 (2025), 113553
Martin Sýkora, Michal Pavelka, Ilya Peshkov, Piotr Minakowski, Václav Klika, Evgeniy Romenski, “Comparison of the symmetric hyperbolic thermodynamically compatible framework with Hamiltonian mechanics of binary mixtures”, Continuum Mech. Thermodyn., 2024
S.K. Godunov, “Memoirs of Finite Difference schemes”, Journal of Computational Physics, 2024, 113522
E. I. Romenski, I. M. Peshkov, “Thermodynamically Compatible Hyperbolic Model for a Two-Phase Compressible Fluid Flow with Surface Tension”, Fluid Dyn, 58:7 (2023), 1255
E. Romenski, I. Peshkov, “Thermodynamically Compatible Hyperbolic Model for Two-Phase Compressible Fluid Flow with Surface Tension”, Prikladnaâ matematika i mehanika, 87:2 (2023), 211
Markus Hütter, Michal Pavelka, “Particle-based approach to the Eulerian distortion field and its dynamics”, Continuum Mech. Thermodyn., 35:5 (2023), 1943
Martin Sýkora, Michal Pavelka, Liliana Restuccia, David Jou, “Multiscale heat transport with inertia and thermal vortices”, Phys. Scr., 98:10 (2023), 105234
Simone Chiocchetti, Michael Dumbser, “An Exactly Curl-Free Staggered Semi-Implicit Finite Volume Scheme for a First Order Hyperbolic Model of Viscous Two-Phase Flows with Surface Tension”, J Sci Comput, 94:1 (2023)
Evgeniy Romenski, Galina Reshetova, Ilya Peshkov, “Two-phase hyperbolic model for porous media saturated with a viscous fluid and its application to wavefields simulation”, Applied Mathematical Modelling, 106 (2022), 567
Evgeniy Romenski, Galina Reshetova, Lecture Notes in Computer Science, 13376, Computational Science and Its Applications – ICCSA 2022, 2022, 303
Ferdinand Thein, Evgeniy Romenski, Michael Dumbser, “Exact and Numerical Solutions of the Riemann Problem for a Conservative Model of Compressible Two-Phase Flows”, J Sci Comput, 93:3 (2022)
Petr Vágner, Michal Pavelka, Jürgen Fuhrmann, Václav Klika, “A multiscale thermodynamic generalization of Maxwell-Stefan diffusion equations and of the dusty gas model”, International Journal of Heat and Mass Transfer, 199 (2022), 123405
Sykora M., Pavelka M., La Mantia M., Jou D., Grmela M., “On the Relations Between Large-Scale Models of Superfluid Helium-4”, Phys. Fluids, 33:12 (2021), 127124
Gabriel A.-A., Li D., Chiocchetti S., Tavelli M., Peshkov I., Romenski E., Dumbser M., “A Unified First-Order Hyperbolic Model For Nonlinear Dynamic Rupture Processes in Diffuse Fracture Zones”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 379:2196 (2021), 20200130
Chiocchetti S., Peshkov I., Gavrilyuk S., Dumbser M., “High Order Ader Schemes and Glm Curl Cleaning For a First Order Hyperbolic Formulation of Compressible Flow With Surface Tension”, J. Comput. Phys., 426 (2021), 109898
Boscheri W., Dumbser M., Ioriatti M., Peshkov I., Romenski E., “A Structure-Preserving Staggered Semi-Implicit Finite Volume Scheme For Continuum Mechanics”, J. Comput. Phys., 424 (2021), 109866
Pavelka M., Peshkov I., Klika V., “on Hamiltonian Continuum Mechanics”, Physica D, 408 (2020), 132510
Romenski E., Reshetova G., Peshkov I., Dumbser M., “Modeling Wavefields in Saturated Elastic Porous Media Based on Thermodynamically Compatible System Theory For Two-Phase Solid-Fluid Mixtures”, Comput. Fluids, 206 (2020), 104587
Romenski E., Peshkov I., Dumbser M., Fambri F., “a New Continuum Model For General Relativistic Viscous Heat-Conducting Media”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 378:2170, SI (2020), 20190175
Busto S., Chiocchetti S., Dumbser M., Gaburro E., Peshkov I., “High Order Ader Schemes For Continuum Mechanics”, Front. Physics, 8 (2020), 32
Цитирование в формате AMSBIB
Обратная связь: