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Journal articles on the topic 'Incompressible Euler system'

Author: Grafiati

Published: 14 March 2023

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1

Wang, Shu, Jianwei Yang, and Dang Luo. "Convergence of compressible Euler–Poisson system to incompressible Euler equations." Applied Mathematics and Computation 216, no. 11 (August 2010): 3408–18. http://dx.doi.org/10.1016/j.amc.2010.04.035.

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2

Masmoudi, Nader. "FROM VLASOV-POISSON SYSTEM TO THE INCOMPRESSIBLE EULER SYSTEM." Communications in Partial Differential Equations 26, no. 9-10 (September 1, 2001): 1913–28. http://dx.doi.org/10.1081/pde-100107463.

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3

Hmidi, Taoufik, and Samira Sulaiman. "Incompressible limit for the two-dimensional isentropic Euler system with critical initial data." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 6 (December 2014): 1127–54. http://dx.doi.org/10.1017/s0308210512000509.

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We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space . By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

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4

Wu, Weijun, Fujun Zhou, and Yongsheng Li. "Incompressible Euler–Poisson limit of the Vlasov–Poisson–Boltzmann system." Journal of Mathematical Physics 63, no. 8 (August 1, 2022): 081502. http://dx.doi.org/10.1063/5.0054024.

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This paper is to justify the incompressible Euler–Poisson limit of the Vlasov–Poisson–Boltzmann system in the incompressible hyperbolic regime. The proof is based on a new [Formula: see text] framework, which consists of the [Formula: see text] energy estimate and the weighted [Formula: see text] estimate of the Vlasov–Poisson–Boltzmann system.

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5

Shi, Fei. "Incompressible limit of Euler equations with damping." Electronic Research Archive 30, no. 1 (2021): 126–39. http://dx.doi.org/10.3934/era.2022007.

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<abstract><p>The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.</p></abstract>

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6

Yang, Jianwei, and Hongli Wang. "Convergence of a Singular Euler-Maxwell Approximation of the Incompressible Euler Equations." Journal of Applied Mathematics 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/942024.

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This paper studies the Euler-Maxwell system which is a model of a collisionless plasma. By energy estimation and the curl-div decomposition of the gradient, we rigorously justify a singular approximation of the incompressible Euler equations via a quasi-neutral regime.

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7

Liu, Chundi, and Boyi Wang. "Quasineutral limit for a model of three-dimensional Euler–Poisson system with boundary." Analysis and Applications 16, no. 02 (February 5, 2018): 283–305. http://dx.doi.org/10.1142/s0219530517500051.

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Quasineutral limit for a model of three-dimensional Euler–Poisson system in half space with a boundary layer is studied. Based on the matched asymptotic expansion method of singular perturbation problem and the elaborate energy method, we prove that the quasineutral regime is the incompressible Euler equation.

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8

Saint Raymond, X. "Remarks on axisymmetric solutions of the incompressible euler system." Communications in Partial Differential Equations 19, no. 1-2 (January 1994): 321–34. http://dx.doi.org/10.1080/03605309408821018.

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9

FERNÁNDEZ, MIGUEL A., and MARWAN MOUBACHIR. "SENSITIVITY ANALYSIS FOR AN INCOMPRESSIBLE AEROELASTIC SYSTEM." Mathematical Models and Methods in Applied Sciences 12, no. 08 (August 2002): 1109–30. http://dx.doi.org/10.1142/s0218202502002094.

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This paper deals with problems arising in the sensitivity analysis for fluid-structure interaction systems. Our model consists of a fluid described by the incompressible Navier–Stokes equations interacting with a solid under large deformations. We obtain a linearized problem which allow us to compute the derivative of the state variable with respect to a given boundary parameter. We use a particular definition of the first-order correction for the perturbed state and consider a weak arbitrary Euler–Lagrange formulation for the coupled system.

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10

Wang, Shu, and Yongxin Wang. "The Global Well-Posedness for Large Amplitude Smooth Solutions for 3D Incompressible Navier–Stokes and Euler Equations Based on a Class of Variant Spherical Coordinates." Mathematics 8, no. 7 (July 21, 2020): 1195. http://dx.doi.org/10.3390/math8071195.

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This paper investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the three-dimensional (3D) incompressible Navier–Stokes (NS) and Euler systems. The global well-posedness for large amplitude smooth solutions to the Cauchy problem for 3D incompressible NS and Euler equations based on a class of variant spherical coordinates is obtained, where smooth initial data is not axi-symmetric with respect to any coordinate axis in Cartesian coordinate system. Furthermore, we establish the existence, uniqueness and exponentially decay rate in time of the global strong solution to the initial boundary value problem for 3D incompressible NS equations for a class of the smooth large initial data and a class of the special bounded domain described by variant spherical coordinates.

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11

SAINTE-MARIE, JACQUES. "VERTICALLY AVERAGED MODELS FOR THE FREE SURFACE NON-HYDROSTATIC EULER SYSTEM: DERIVATION AND KINETIC INTERPRETATION." Mathematical Models and Methods in Applied Sciences 21, no. 03 (March 2011): 459–90. http://dx.doi.org/10.1142/s0218202511005118.

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Starting from the Euler equations for incompressible flows, we propose an extension of the classical Saint-Venant system where the non-hydrostatic pressure terms are taken into account in the asymptotic expansion. We also derive a multilayer version of this vertically averaged Euler system. The multilayer approach allows mass exchanges between the neighboring layers. Finally we give a kinetic type interpretation for the proposed models.

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12

PENG, YUE-JUN, and INGRID VIOLET. "ASYMPTOTIC EXPANSIONS IN A STEADY STATE EULER–POISSON SYSTEM AND CONVERGENCE TO INCOMPRESSIBLE EULER EQUATIONS." Mathematical Models and Methods in Applied Sciences 15, no. 05 (May 2005): 717–36. http://dx.doi.org/10.1142/s0218202505000546.

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This work is concerned with a steady state Euler–Poisson system for potential flows arising in mathematical modeling for plasmas and semiconductors. We study the zero electron mass limit and zero relaxation time limit of the system by using the method of asymptotic expansions. These two limits are expressed by the Maxwell–Boltzmann relation and the classical drift-diffusion model, respectively. For each limit, we show the existence and uniqueness of profiles and justify the asymptotic expansions up to any order. These results also give new approaches for the convergence of the Euler–Poisson system to incompressible Euler equations, which has already been obtained via the quasi-neutral limit.

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13

Yang, Jianwei, Mengyu Liu, and Huiyun Hao. "Inviscid, zero Froude number limit of the viscous shallow water system." Open Mathematics 19, no. 1 (January 1, 2021): 531–39. http://dx.doi.org/10.1515/math-2021-0043.

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Abstract In this paper, we study the inviscid and zero Froude number limits of the viscous shallow water system. We prove that the limit system is represented by the incompressible Euler equations on the whole space. Furthermore, the rate of convergence is also obtained.

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14

Puel, Marjolaine. "CONVERGENCE OF THE SCHRÖDINGER–POISSON SYSTEM TO THE INCOMPRESSIBLE EULER EQUATIONS." Communications in Partial Differential Equations 27, no. 11-12 (December 31, 2002): 2311–31. http://dx.doi.org/10.1081/pde-120016159.

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15

Brenier, Y. "convergence of the vlasov-poisson system to the incompressible euler equations." Communications in Partial Differential Equations 25, no. 3-4 (January 2000): 737–54. http://dx.doi.org/10.1080/03605300008821529.

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16

Nersisyan, Hayk. "Stabilization of the 2D incompressible Euler system in an infinite strip." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 30, no. 4 (July 2013): 737–62. http://dx.doi.org/10.1016/j.anihpc.2012.12.002.

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17

Camassa, R., S. Chen, G. Falqui, G. Ortenzi, and M. Pedroni. "An inertia ‘paradox’ for incompressible stratified Euler fluids." Journal of Fluid Mechanics 695 (February 16, 2012): 330–40. http://dx.doi.org/10.1017/jfm.2012.23.

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AbstractThe interplay between incompressibility and stratification can lead to non-conservation of horizontal momentum in the dynamics of a stably stratified incompressible Euler fluid filling an infinite horizontal channel between rigid upper and lower plates. Lack of conservation occurs even though in this configuration only vertical external forces act on the system. This apparent paradox was seemingly first noticed by Benjamin (J. Fluid Mech., vol. 165, 1986, pp. 445–474) in his classification of the invariants by symmetry groups with the Hamiltonian structure of the Euler equations in two-dimensional settings, but it appears to have been largely ignored since. By working directly with the motion equations, the paradox is shown here to be a consequence of the rigid lid constraint coupling through incompressibility with the infinite inertia of the far ends of the channel, assumed to be at rest in hydrostatic equilibrium. Accordingly, when inertia is removed by eliminating the stratification, or, remarkably, by using the Boussinesq approximation of uniform density for the inertia terms, horizontal momentum conservation is recovered. This interplay between constraints, action at a distance by incompressibility, and inertia is illustrated by layer-averaged exact results, two-layer long-wave models, and direct numerical simulations of the incompressible Euler equations with smooth stratification.

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18

An, Shangyong, and Qian Zhang. "On the Blowup for the 3D Axisymmetric Incompressible Chemotaxis-Euler Equations." Journal of Function Spaces 2021 (April 5, 2021): 1–9. http://dx.doi.org/10.1155/2021/5541713.

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In this paper, we investigate the 3D incompressible chemotaxis-Euler equations. Taking advantage of the structure of axisymmetric fluids, we establish the blowup criterion of the system using the Fourier localization method.

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19

Wei, Zhiqiang, and Jianwei Yang. "On a Quasi-Neutral Approximation of the Incompressible Navier-Stokes Equations." ISRN Applied Mathematics 2012 (November 5, 2012): 1–7. http://dx.doi.org/10.5402/2012/581710.

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This paper considers a pressureless Euler-Poisson system with viscosity in plasma physics in the torus . We give a rigorous justification of its asymptotic limit toward the incompressible Navier Stokes equations via quasi-neutral regime using the modulated energy method.

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20

Loeper, G. "A Fully Nonlinear Version of the Incompressible Euler Equations: The Semigeostrophic System." SIAM Journal on Mathematical Analysis 38, no. 3 (January 2006): 795–823. http://dx.doi.org/10.1137/050629070.

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21

Hsiao, Ling, Fu Cai Li, and Shu Wang. "Convergence of the Vlasov–Poisson–Boltzmann System to the Incompressible Euler Equations." Acta Mathematica Sinica, English Series 23, no. 4 (May 5, 2006): 761–68. http://dx.doi.org/10.1007/s10114-005-0774-3.

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22

You, Xiaoguang. "Vanishing viscosity limit of incompressible flow around a small obstacle: A special case." AIMS Mathematics 8, no. 2 (2022): 2611–21. http://dx.doi.org/10.3934/math.2023135.

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<abstract><p>In this paper, we consider two dimensional viscous flow around a small obstacle. In <sup>[<xref ref-type="bibr" rid="b4">4</xref>]</sup>, the authors proved that the solutions of the Navier-Stokes system around a small obstacle of size $ \varepsilon $ converge to solutions of the Euler system in the whole space under the condition that the size of the obstacle $ \varepsilon $ is smaller than a suitable constant $ K $ times the kinematic viscosity $ \nu $. We show that, if the Euler flow is antisymmetric, then this smallness condition can be removed.</p></abstract>

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23

Haack, Jeffrey, Shi Jin, and Jian‐Guo Liu. "An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations." Communications in Computational Physics 12, no. 4 (October 2012): 955–80. http://dx.doi.org/10.4208/cicp.250910.131011a.

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AbstractThe computation of compressible flows becomes more challenging when the Mach number has different orders of magnitude. When the Mach number is of order one, modern shock capturing methods are able to capture shocks and other complex structures with high numerical resolutions. However, if the Mach number is small, the acoustic waves lead to stiffness in time and excessively large numerical viscosity, thus demanding much smaller time step and mesh size than normally needed for incompressible flow simulation. In this paper, we develop an all-speed asymptotic preserving (AP) numerical scheme for the compressible isentropic Euler and Navier-Stokes equations that is uniformly stable and accurate for all Mach numbers. Our idea is to split the system into two parts: one involves a slow, nonlinear and conservative hyperbolic system adequate for the use of modern shock capturing methods and the other a linear hyperbolic system which contains the stiff acoustic dynamics, to be solved implicitly. This implicit part is reformulated into a standard pressure Poisson projection system and thus possesses sufficient structure for efficient fast Fourier transform solution techniques. In the zero Mach number limit, the scheme automatically becomes a projection method-like incompressible solver. We present numerical results in one and two dimensions in both compressible and incompressible regimes.

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24

De Rosa, Luigi, and Silja Haffter. "Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations." Nonlinearity 35, no. 10 (September 2, 2022): 5150–92. http://dx.doi.org/10.1088/1361-6544/ac8a39.

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Abstract For β < 1 3 , we consider C β T 3 × [ 0 , T ] weak solutions of the incompressible Euler equations that do not conserve the kinetic energy. We prove that for such solutions the closed and non-empty set of singular times B satisfies dim H ( B ) ⩾ 2 β 1 − β . This lower bound on the Hausdorff dimension of the singular set in time is intrinsically linked to the Hölder regularity of the kinetic energy and we conjecture it to be sharp. As a first step in this direction, for every β < β ′ < 1 3 we are able to construct, via a convex integration scheme, non-conservative C β T 3 × [ 0 , T ] weak solutions of the incompressible Euler system such that dim H ( B ) ⩽ 1 2 + 1 2 2 β ′ 1 − β ′ . The structure of the wild solutions that we build allows moreover to deduce non-uniqueness of C β T 3 × [ 0 , T ] weak solutions of the Cauchy problem for Euler from every smooth initial datum.

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25

Ha, Seung-Yeal, Moon-Jin Kang, and Bongsuk Kwon. "A hydrodynamic model for the interaction of Cucker–Smale particles and incompressible fluid." Mathematical Models and Methods in Applied Sciences 24, no. 11 (August 6, 2014): 2311–59. http://dx.doi.org/10.1142/s0218202514500225.

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We present a new hydrodynamic model for the interactions between collision-free Cucker–Smale flocking particles and a viscous incompressible fluid. Our proposed model consists of two hydrodynamic models. For the Cucker–Smale flocking particles, we employ the pressureless Euler system with a non-local flocking dissipation, whereas for the fluid, we use the incompressible Navier–Stokes equations. These two hydrodynamic models are coupled through a drag force, which is the main flocking mechanism between the particles and the fluid. The flocking mechanism between particles is regulated by the Cucker–Smale model, which accelerates global flocking between the particles and the fluid. We show that this model admits the global-in-time classical solutions, and exhibits time-asymptotic flocking, provided that the initial data is appropriately small. In the course of our analysis for the proposed system, we first consider the hydrodynamic Cucker–Smale equations (the pressureless Euler system with a non-local flocking dissipation), for which the global existence and the time-asymptotic behavior of the classical solutions are also investigated.

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26

Wang, Hongli, and Jianwei Yang. "INVISCID QUASI-NEUTRAL LIMIT OF A NAVIER-STOKES-POISSON-KORTEWEG SYSTEM." Mathematical Modelling and Analysis 23, no. 2 (April 18, 2018): 205–16. http://dx.doi.org/10.3846/mma.2018.013.

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The combined quasi-neutral and inviscid limit of the Navier-Stokes-Poisson-Korteweg system with density-dependent viscosity and cold pressure in the torus T3 is studied. It is shown that, for the well-prepared initial data, the global weak solution of the Navier-Stokes-Poisson-Korteweg system converges strongly to the strong solution of the incompressible Euler equations when the Debye length and the viscosity coeﬃcient go to zero simultaneously. Furthermore, the rate of convergence is also obtained.

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27

Wang, Shu, and Song Jiang. "The Convergence of the Navier–Stokes–Poisson System to the Incompressible Euler Equations." Communications in Partial Differential Equations 31, no. 4 (January 2006): 571–91. http://dx.doi.org/10.1080/03605300500361487.

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28

Kwon, Young-Sam. "From the degenerate quantum compressible Navier-Stokes-Poisson system to incompressible Euler equations." Journal of Mathematical Physics 59, no. 12 (December 2018): 123101. http://dx.doi.org/10.1063/1.4996942.

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29

Xiao, Ling, Fucai Li, and Shu Wang. "Convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations." Science in China Series A 49, no. 2 (January 2006): 255–66. http://dx.doi.org/10.1007/s11425-005-0062-9.

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30

Brenier, Yann, Norbert Mauser, and Marjolaine Puel. "Incompressible Euler and E-MHD as scaling limits of the Vlasov-Maxwell system." Communications in Mathematical Sciences 1, no. 3 (2003): 437–47. http://dx.doi.org/10.4310/cms.2003.v1.n3.a4.

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31

Parseh, Kaveh, and Kazem Hejranfar. "Assessment of Characteristic Boundary Conditions Based on the Artificial Compressibility Method in Generalized Curvilinear Coordinates for Solution of the Euler Equations." Computational Methods in Applied Mathematics 18, no. 4 (October 1, 2018): 717–40. http://dx.doi.org/10.1515/cmam-2017-0048.

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AbstractThe characteristic boundary conditions are applied and assessed for the solution of incompressible inviscid flows. The two-dimensional incompressible Euler equations based on the artificial compressibility method are considered and then the characteristic boundary conditions are formulated in the generalized curvilinear coordinates and implemented on both the far-field and wall boundaries. A fourth-order compact finite-difference scheme is used to discretize the resulting system of equations. The solution methodology adopted is more suitable for this assessment because the Euler equations and the high-accurate numerical scheme applied are quite sensitive to the treatment of boundary conditions. Two benchmark test cases are computed to investigate the accuracy and performance of the characteristic boundary conditions implemented compared to the simplified boundary conditions. The sensitivity of the solution obtained by applying the characteristic boundary conditions to the different numerical parameters is also studied. Indications are that the characteristic boundary conditions applied improve the accuracy and the convergence rate of the solution compared to the simplified boundary conditions.

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32

Kotsur, O. S., G. A. Shcheglov, and I. K. Marchevsky. "Approximate Weak Solutions to the Vorticity Evolution Equation for a Viscous Incompressible Fluid in the Class of Vortex Filaments." Nelineinaya Dinamika 18, no. 3 (2022): 423–39. http://dx.doi.org/10.20537/nd220307.

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This paper is concerned with the equation for the evolution of vorticity in a viscous incompressible fluid, for which approximate weak solutions are sought in the class of vortex filaments. In accordance with the Helmholtz theorem, a system of vortex filaments that is transferred by the flow of an ideal barotropic fluid is an exact solution to the Euler equation. At the same time, for viscous incompressible flows described by the system of Navier – Stokes equations, the search for such generalized solutions in the finite time interval is generally difficult. In this paper, we propose a method for transforming the diffusion term in the vorticity evolution equation that makes it possible to construct its approximate solution in the class of vortex filaments under the assumption that there is no helicity of vorticity. Such an approach is useful in constructing vortex methods of computational hydrodynamics to model viscous incompressible flows.

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33

GOLSE, F., and L. SAINT-RAYMOND. "THE VLASOV–POISSON SYSTEM WITH STRONG MAGNETIC FIELD IN QUASINEUTRAL REGIME." Mathematical Models and Methods in Applied Sciences 13, no. 05 (May 2003): 661–714. http://dx.doi.org/10.1142/s0218202503002647.

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Consider the motion of a gas of electrons with a background of ions, subject to the self-consistent electric field and to a constant external magnetic field. As the Debye length and the Larmor radius vanish at the same rate, the asymptotic current density is governed by the 2D1/2 incompressible Euler equation. Establishing limit requires to overcome various difficulties: compactness with respect to the space variable, control of large velocities, oscillations in the time variable. Yet, for particular initial data, the simultaneous gyrokinetic and quasineutral approximation is completely justified.

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34

Ju, Qiangchang, Yong Li, and Shu Wang. "Rate of convergence from the Navier–Stokes–Poisson system to the incompressible Euler equations." Journal of Mathematical Physics 50, no. 1 (January 2009): 013533. http://dx.doi.org/10.1063/1.3054866.

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35

Feireisl, Eduard, and Antonín Novotný. "Inviscid Incompressible Limits Under Mild Stratification: A Rigorous Derivation of the Euler–Boussinesq System." Applied Mathematics & Optimization 70, no. 2 (March 25, 2014): 279–307. http://dx.doi.org/10.1007/s00245-014-9243-7.

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36

Donatelli, Donatella, Eduard Feireisl, and Antonín Novotný. "Scale analysis of a hydrodynamic model of plasma." Mathematical Models and Methods in Applied Sciences 25, no. 02 (November 24, 2014): 371–94. http://dx.doi.org/10.1142/s021820251550013x.

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We examine a hydrodynamic model of the motion of ions in plasma in the regime of small Debye length, a small ratio of the ion/electron temperature, and high Reynolds number. We analyze the associated singular limit and identify the limit problem — the incompressible Euler system. The result leans on careful analysis of the oscillatory component of the solutions by means of Fourier analysis.

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37

Hsu, Uzu Kuei, Chang Hsien Tai, and Chien Hsiung Tsai. "All Speed and High-Resolution Scheme Applied to Three-Dimensional Multi-Block Complex Flowfield System." Journal of Mechanics 20, no. 1 (March 2004): 13–25. http://dx.doi.org/10.1017/s1727719100004007.

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ABSTRACTThe improved numerical approach is implemented with preconditioned Navier-Stokes solver on arbitrary three-dimensional (3-D) structured multi-block complex flowfield. With the successful application of time-derivative preconditioning, present hybrid finite volume solver is performed to obtain the steady state solutions in compressible and incompressible flows. This solver which combined the adjective upwind splitting method (AUSM) family of low-diffusion flux-splitting scheme with an optimally smoothing multistage scheme and the time-derivative preconditioning is used to solve both the compressible and incompressible Euler and Navier-Stokes equations. In addition, a smoothing procedure is used to provide a mechanism for controlling the numerical implementation to avoid the instability at stagnation and sonic region. The effects of preconditioning on accuracy and convergence to the steady state of the numerical solutions are presented. There are two validation cases and three complex cases simulated as shown in this study. The numerical results obtained for inviscid and viscous two-dimensional flows over a NACA0012 airfoil at free stream Mach number ranging from 0.1 to 1.0E-7 indicates that efficient computations of flows with very low Mach numbers are now possible, without losing accuracy. And it is effectively to simulate 3-D complex flow phenomenon from compressible flow to incompressible by using the advanced numerical methods.

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38

Ershkov, Sergey V., Alla Rachinskaya, Evgenii Yu Prosviryakov, and Roman V. Shamin. "On the Semi-Analytical Solutions in Hydrodynamics of Ideal Fluid Flows Governed by Large-Scale Coherent Structures of Spiral-Type." Symmetry 13, no. 12 (December 3, 2021): 2307. http://dx.doi.org/10.3390/sym13122307.

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We have presented here a clearly formulated algorithm or semi-analytical solving procedure for obtaining or tracing approximate hydrodynamical fields of flows (and thus, videlicet, their trajectories) for ideal incompressible fluids governed by external large-scale coherent structures of spiral-type, which can be recognized as special invariant at symmetry reduction. Examples of such structures are widely presented in nature in “wind-water-coastline” interactions during a long-time period. Our suggested mathematical approach has obvious practical meaning as tracing process of formation of the paths or trajectories for material flows of fallout descending near ocean coastlines which are forming its geometry or bottom surface of the ocean. In our presentation, we explore (as first approximation) the case of non-stationary flows of Euler equations for incompressible fluids, which should conserve the Bernoulli-function as being invariant for the aforementioned system. The current research assumes approximated solution (with numerical findings), which stems from presenting the Euler equations in a special form with a partial type of approximated components of vortex field in a fluid. Conditions and restrictions for the existence of the 2D and 3D non-stationary solutions of the aforementioned type have been formulated as well.

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39

Kwon, Young‐Sam, and Fucai Li. "Convergence of the two‐fluid compressible Navier–Stokes–Poisson system to the incompressible Euler equations." Mathematical Methods in the Applied Sciences 43, no. 10 (March 31, 2020): 6262–75. http://dx.doi.org/10.1002/mma.6369.

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40

Tokareva, Margarita, and Alexander Papin. "On the existence of global solution of the system of equations of liquid movement in porous medium." E3S Web of Conferences 234 (2021): 00095. http://dx.doi.org/10.1051/e3sconf/202123400095.

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The initial-boundary value problem for the system of one-dimensional isothermal motion of viscous liquid in deformable viscous porous medium is considered. Local theorem of existence and uniqueness of problem is proved in case of compressible liquid. In case of incompressible liquid the theorem of global solvability in time is proved in Holder classes. A feature of the model of fluid filtration in a porous medium considered in this paper is the inclusion of the mobility of the solid skeleton and its poroelastiс properties. The transition from Euler variables to Lagrangian variables is used in the proof of the theorems.

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41

Tang, Qili. "A parallel finite element algorithm for nonstationary incompressible magnetohydrodynamics equations." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 7 (July 2, 2018): 1579–95. http://dx.doi.org/10.1108/hff-06-2017-0251.

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Purpose The purpose of this paper is to design a parallel finite element (FE) algorithm based on fully overlapping domain decomposition for solving the nonstationary incompressible magnetohydrodynamics (MHD). Design/methodology/approach The fully discrete Euler implicit/explicit FE subproblems, which are defined in the whole domain with vast majority of the degrees of freedom associated with the particular subdomain, are solved in parallel. In each subproblem, the linear term is treated by implicit scheme and the nonlinear term is solved by explicit one. Findings For the algorithm, the almost unconditional convergence with optimal orders is validated by numerical tests. Some interesting phenomena are presented. Originality/value The proposed algorithm is effective, easy to realize with low communication costs and preferred for solving the strong nonlinear MHD system.

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42

CAMASSA, R., P. O. RUSÅS, A. SAXENA, and R. TIRON. "Fully nonlinear periodic internal waves in a two-fluid system of finite depth." Journal of Fluid Mechanics 652 (May 19, 2010): 259–98. http://dx.doi.org/10.1017/s0022112010000054.

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Periodic travelling wave solutions for a strongly nonlinear model of long internal wave propagation in a two-fluid system are derived and extensively analysed, with the aim of providing structure to the rich parametric space of existence of such waves for the parent Euler system. The waves propagate at the interface between two homogeneous-density incompressible fluids filling the two-dimensional domain between rigid planar boundaries. The class of waves with a prescribed mean elevation, chosen to coincide with the origin of the vertical (parallel to gravity) axis, and prescribed zero period-average momentum and volume-flux is studied in detail. The constraints are selected because of their physical interpretation in terms of possible processes of wave generation in wave-tanks, and give rise to a quadrature formula which is analysed in parameter space with a combination of numerical and analytical tools. The resulting model solutions are validated against those computed numerically from the parent Euler two-layer system with a boundary element method. The parametric domain of existence of model periodic waves is determined in closed form by curves in the amplitude–speed (A, c) parameter plane corresponding to infinite period limiting cases of fronts (conjugate states) and solitary waves. It is found that the existence domain of Euler solutions is a subset of that of the model. A third closed form relation between c and A indicates where the Euler solutions cease to exist within the model's domain, and this is related to appearance of ‘overhanging’ (multiple valued) wave profiles. The model existence domain is further partitioned in regions where the model is expected to provide accurate approximations to Euler solutions based on analytical estimates from the quadrature. The resulting predictions are found to be in good agreement with the numerical Euler solutions, as exhibited by several wave properties, including kinetic and potential energy, over a broad range of parameter values, extending to the limiting cases of critical depth ratio and extreme density ratios. In particular, when the period is sufficiently long, model solutions show that for a given supercritical speed waves of substantially larger amplitude than the limiting amplitude of solitary waves can exist, and are good approximations of the corresponding Euler solutions. This finding can be relevant for modelling field observations of oceanic internal waves, which often occur in wavetrains with multiple peaks.

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Beaume, Cédric. "Adaptive Stokes Preconditioning for Steady Incompressible Flows." Communications in Computational Physics 22, no. 2 (June 21, 2017): 494–516. http://dx.doi.org/10.4208/cicp.oa-2016-0201.

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AbstractThis paper describes an adaptive preconditioner for numerical continuation of incompressible Navier–Stokes flows based on Stokes preconditioning [42] which has been used successfully in studies of pattern formation in convection. The preconditioner takes the form of the Helmholtz operator I–ΔtL which maps the identity (no preconditioner) for Δt≪1 to Laplacian preconditioning for Δt≫1. It is built on a first order Euler time-discretization scheme and is part of the family of matrix-free methods. The preconditioner is tested on two fluid configurations: three-dimensional doubly diffusive convection and a two-dimensional projection of a shear flow. In the former case, it is found that Stokes preconditioning is more efficient for , away from the values used in the literature. In the latter case, the simple use of the preconditioner is not sufficient and it is necessary to split the system of equations into two subsystems which are solved simultaneously using two different preconditioners, one of which is parameter dependent. Due to the nature of these applications and the flexibility of the approach described, this preconditioner is expected to help in a wide range of applications.

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Dutrifoy, Alexandre, and Taoufik Hmidi. "The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data." Comptes Rendus Mathematique 336, no. 6 (March 2003): 471–74. http://dx.doi.org/10.1016/s1631-073x(03)00100-6.

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Ohkitani, K. "Numerical study on the incompressible Euler equations as a Hamiltonian system: Sectional curvature and Jacobi field." Physics of Fluids 22, no. 5 (May 2010): 057101. http://dx.doi.org/10.1063/1.3407673.

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Dutrifoy, Alexandre, and Taoufik Hmidi. "The incompressible limit of solutions of the two-dimensional compressible Euler system with degenerating initial data." Communications on Pure and Applied Mathematics 57, no. 9 (2004): 1159–77. http://dx.doi.org/10.1002/cpa.20026.

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DANCHIN, RAPHAËL, and MARIUS PAICU. "GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO." Mathematical Models and Methods in Applied Sciences 21, no. 03 (March 2011): 421–57. http://dx.doi.org/10.1142/s0218202511005106.

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Models with a vanishing anisotropic viscosity in the vertical direction are of relevance for the study of turbulent flows in geophysics. This motivates us to study the two-dimensional Boussinesq system with horizontal viscosity in only one equation. In this paper, we focus on the global existence issue for possibly large initial data. We first examine the case where the Navier–Stokes equation with no vertical viscosity is coupled with a transport equation. Second, we consider a coupling between the classical two-dimensional incompressible Euler equation and a transport–diffusion equation with diffusion in the horizontal direction only. For both systems, we construct global weak solutions à la Leray and strong unique solutions for more regular data. Our results rest on the fact that the diffusion acts perpendicularly to the buoyancy force.

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Gavrilyuk, Sergey. "‘Uncertainty’ principle in two fluid–mechanics." ESAIM: Proceedings and Surveys 69 (2020): 47–55. http://dx.doi.org/10.1051/proc/202069047.

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Hamilton’s principle (or principle of stationary action) is one of the basic modelling tools in finite-degree-of-freedom mechanics. It states that the reversible motion of mechanical systems is completely determined by the corresponding Lagrangian which is the difference between kinetic and potential energy of our system. The governing equations are the Euler-Lagrange equations for Hamil- ton’s action. Hamilton’s principle can be naturally extended to both one-velocity and multi-velocity continuum mechanics (infinite-degree-of-freedom systems). In particular, the motion of multi–velocity continuum is described by a coupled system of ‘Newton’s laws’ (Euler-Lagrange equations) for each component. The introduction of dissipative terms compatible with the second law of thermodynamics and a natural restriction on the behaviour of potential energy (convexity) allows us to derive physically reasonable and mathematically well posed governing equations. I will consider a simplest example of two-velocity fluids where one of the phases is incompressible (for example, flow of dusty air, or flow of compressible bubbles in an incompressible fluid). A very surprising fact is that one can obtain different governing equations from the same Lagrangian. Different types of the governing equations are due to the choice of independent variables and the corresponding virtual motions. Even if the total momentum and total energy equations are the same, the equations for individual components differ from each other by the presence or absence of gyroscopic forces (also called ‘lift’ forces). These forces have no influence on the hyperbolicity of the governing equations, but can drastically change the distribution of density and velocity of components. To the best of my knowledge, such an uncertainty in obtaining the governing equations of multi- phase flows has never been the subject of discussion in a ‘multi-fluid’ community.

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Zaytsev, Maksim, and Vyacheslav Akkerman. "Explicit Representation of the Euler and Navier – Stokes Equations of Incompressible Fluid with Reduced Dimensionality in Integral Form." Mathematical Physics and Computer Simulation, no. 1 (April 2022): 5–20. http://dx.doi.org/10.15688/mpcm.jvolsu.2022.1.1.

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In this paper, we have obtained “stationary” systems of integraldifferential equations, which are consequences of the non-stationary Euler and Navier - Stokes equations of an incompressible fluid, and for which there are no time derivatives. If we set a correct problem for them, then we can determine the entire non-stationary flow in the volume without solving the nonstationary problem. It is enough to specify time-varying data only on some surface of this stream. The method of reduction of overdetermined systems of differential equations, proposed earlier by the authors, is used. In this method, in the case of a successful choice of the additional constraint equation, the overdetermined systems of differential equations are reduced to PDE systems of dimension less than that of the original PDE systems. The Euler and Navier-Stokes equations themselves act as the constraint equations, and the dimension is reduced for the integral equations, which are obtained using the Helmholtz theorem on the expansion of an arbitrary vector field into vortex and potential components. The peculiarity of this work lies in the fact that all the equations reduced in dimension are obtained in an explicit form, in contrast to the previous works of the authors, where up to 200–300 equations with reduced dimensions were proposed. In reduced systems of integral-differential equations, there is integration over space, therefore, reduction over spatial variables by given method is impossible. If this method is generalized a little, then we can obtain a reduced system of integral equations, where the unknowns have no derivatives with respect to space, but integration over space remains. Non-stationary new integral equations are also obtained, which determine the evolution of the flow. In Appendices A and B, sufficient conditions for the correctness of the reduced system of integral-differential equations are derived. Conditions are found under which the Euler equations follow directly from these reduced equations. It is shown how the time-varying data on some surface of this stream should be related. The change of variables, which is used in the reduction of the Navier - Stokes equations, is also investigated he resulting integral equations can be used to study complex vortices in the atmosphere. For example, if devices measuring data on its surface are installed on a flying object, then, knowing the vorticity profile ω0(r) at a certain moment in time, it is possible, by solving these equations, to track vortex activity at a distance from this object in real time.

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Gaith, Mohamed. "Flow Induced Vibration of Cantilever Tapered Pipes Transporting Fluid." WSEAS TRANSACTIONS ON FLUID MECHANICS 16 (February 4, 2021): 8–13. http://dx.doi.org/10.37394/232013.2021.16.2.

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A cantilevered tapered slender pipe conveying an incompressible, inviscid fluid of one material is not a conserved system. For certain large fluid velocity, the pipe with uniform cross section would go unstable via flutter Hopf bifurcation. In this paper, the flow induced vibration for cantilever tapering pipe transporting a fluid is presented. Euler Bernoulli and Hamilton’s theories are applied to develop the mathematical model which will be solved using well known Galerkan’s procedure. The effect of smooth tapering of the circular cross sectional area, flow velocity and pipe to fluid mass fraction on the complex natural frequencies and stability will be investigated.

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