Rarefaction Wave

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform

Yi Wang - One of the best experts on this subject based on the ideXlab platform.

  • vanishing viscosity limit to the planar Rarefaction Wave for the two dimensional compressible navier stokes equations
    Communications in Mathematical Physics, 2020
    Co-Authors: Linan Li, Dehua Wang, Yi Wang
    Abstract:

    The vanishing viscosity limit of the two-dimensional (2D) compressible and isentropic Navier–Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar Rarefaction Wave solution. It is proved that there exists a family of smooth solutions for the 2D compressible Navier–Stokes equations converging to the planar Rarefaction Wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficients away from the initial time. In the proof, the hyperbolic Wave is crucially introduced to recover the physical viscosities of the inviscid Rarefaction Wave profile, in order to rigorously justify the vanishing viscosity limit.

  • stability of planar Rarefaction Wave to two dimensional compressible navier stokes equations
    Siam Journal on Mathematical Analysis, 2018
    Co-Authors: Linan Li, Yi Wang
    Abstract:

    It is well known that the Rarefaction Wave, one of the basic Wave patterns of the hyperbolic conservation laws, is nonlinearly stable to the one-dimensional compressible Navier--Stokes equations (cf. [A. Matsumura and K. Nishihara, Japan J. Appl. Math., 3 (1986), pp. 1--13; Comm. Math. Phys., 144 (1992), pp. 325--335; T.-P. Liu and Z. P. Xin, Comm. Math. Phys., 118 (1988), pp. 451--465; K. Nishihara, T. Yang, and H. Zhao, SIAM J. Math. Anal., 35 (2004), pp. 1561--1597]). In the present paper we proved the time-asymptotical nonlinear stability of the planar Rarefaction Wave to the two-dimensional compressible and isentropic Navier--Stokes equations, which gives the first stability result of the planar Rarefaction Wave to the multidimensional system with physical viscosities.

  • stability of planar Rarefaction Wave to 3d full compressible navier stokes equations
    Archive for Rational Mechanics and Analysis, 2018
    Co-Authors: Linan Li, Teng Wang, Yi Wang
    Abstract:

    We prove time-asymptotic stability toward the planar Rarefaction Wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain $${\mathbb{R} \times \mathbb{T}^2}$$ . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying Wave structures, which are crucial for overcoming the difficulties due to the Wave propagation in the transverse directions x2 and x3 and its interactions with the planar Rarefaction Wave in x1 direction.

  • nonlinear stability of planar Rarefaction Wave to the three dimensional boltzmann equation
    arXiv: Analysis of PDEs, 2017
    Co-Authors: Teng Wang, Yi Wang
    Abstract:

    We investigate the time-asymptotic stability of planar Rarefaction Wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [24, 22] and our new observations on the underlying Wave structures of the equation to overcome the difficulties due to the Wave propagation along the transverse directions and its interactions with the planar Rarefaction Wave. Note that this is the first stability result of planar Rarefaction Wave for 3D Boltzmann equation, while the corresponding results for the shock and contact discontinuities are still completely open.

  • Stability of planar Rarefaction Wave to the three-dimensional Boltzmann equation
    2017
    Co-Authors: Teng Wang, Yi Wang
    Abstract:

    We investigate the time-asymptotic stability of planar Rarefaction Wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [18, 16] and our new observations on the underlying Wave structures of the equation to overcome the difficulties due to the Wave propagation along the transverse directions and its interactions with the planar Rarefaction Wave. Note that this is the first stability result of basic Wave patterns for 3D Boltzmann equation.

Yeping Li - One of the best experts on this subject based on the ideXlab platform.

  • asymptotic stability of the Rarefaction Wave for the compressible quantum navier stokes poisson equations
    Journal of Mathematical Analysis and Applications, 2017
    Co-Authors: Yeping Li
    Abstract:

    Abstract In this study, we consider the large time behavior of the solution to the one-dimensional isentropic compressible quantum Navier–Stokes–Poisson equations. The system describes a compressible particle fluid under quantum effects with the potential function of the self-consistent electric field. We show that if the initial data are close to a constant state with asymptotic values at far fields selected such that the Riemann problem on the corresponding Euler system admits a Rarefaction Wave with a strength that is not necessarily small, then the solution exists for all time and it tends to the Rarefaction Wave as t → + ∞ . The proof is based on the energy method by considering the effect of the self-consistent electric field and quantum potential in the viscous compressible fluid. In addition, we compare the quantum compressible Navier–Stokes–Poisson equations and the corresponding compressible Navier–Stokes–Poisson equations based on the large-time behavior of these two classes of models.

  • vanishing viscosity and debye length limit to Rarefaction Wave with vacuum for the 1d bipolar navier stokes poisson equation
    Zeitschrift für Angewandte Mathematik und Physik, 2016
    Co-Authors: Yeping Li
    Abstract:

    In this paper, we consider the one-dimensional (1D) compressible bipolar Navier–Stokes–Poisson equations. We know that when the viscosity coefficient and Debye length are zero in the compressible bipolar Navier–Stokes–Poisson equations, we have the compressible Euler equations. Under the case that the compressible Euler equations have a Rarefaction Wave with one-side vacuum state, we can construct a sequence of the approximation solution to the one-dimensional bipolar Navier–Stokes–Poisson equations with well-prepared initial data, which converges to the above Rarefaction Wave with vacuum as the viscosity and the Debye length tend to zero. Moreover, we also obtain the uniform convergence rate. The results are proved by a scaling argument and elaborate energy estimate.

  • Vanishing viscosity and Debye-length limit to Rarefaction Wave with vacuum for the 1D bipolar Navier–Stokes–Poisson equation
    Zeitschrift für Angewandte Mathematik und Physik, 2016
    Co-Authors: Yeping Li
    Abstract:

    In this paper, we consider the one-dimensional (1D) compressible bipolar Navier–Stokes–Poisson equations. We know that when the viscosity coefficient and Debye length are zero in the compressible bipolar Navier–Stokes–Poisson equations, we have the compressible Euler equations. Under the case that the compressible Euler equations have a Rarefaction Wave with one-side vacuum state, we can construct a sequence of the approximation solution to the one-dimensional bipolar Navier–Stokes–Poisson equations with well-prepared initial data, which converges to the above Rarefaction Wave with vacuum as the viscosity and the Debye length tend to zero. Moreover, we also obtain the uniform convergence rate. The results are proved by a scaling argument and elaborate energy estimate.

A L Velikovich - One of the best experts on this subject based on the ideXlab platform.

  • Analytic theory of Richtmyer–Meshkov instability for the case of reflected Rarefaction Wave
    Physics of Fluids, 1996
    Co-Authors: A L Velikovich
    Abstract:

    An analytic theory of the Richtmyer–Meshkov (RM) instability for the case of reflected Rarefaction Wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock Wave case of the RM instability and for stability analysis of a ‘‘stand‐alone’’ Rarefaction Wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two Rarefaction Waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration o...

  • analytic theory of richtmyer meshkov instability for the case of reflected Rarefaction Wave
    Physics of Fluids, 1996
    Co-Authors: A L Velikovich
    Abstract:

    An analytic theory of the Richtmyer–Meshkov (RM) instability for the case of reflected Rarefaction Wave is presented. The exact solutions of the linearized equations of compressible fluid dynamics are obtained by the method used previously for the reflected shock Wave case of the RM instability and for stability analysis of a ‘‘stand‐alone’’ Rarefaction Wave. The time histories of perturbations and asymptotic growth rates given by the analytic theory are shown to be in good agreement with earlier linear and nonlinear numerical results. Applicability of the prescriptions based on the impulsive model is discussed. The theory is applied to analyze stability of solutions of the Riemann problem, for the case of two Rarefaction Waves emerging after interaction. The RM instability is demonstrated to develop with fully symmetrical initial conditions of the unperturbed Riemann problem, identically zero density difference across the contact interface both before and after interaction, and zero normal acceleration o...

  • instability of a plane centered Rarefaction Wave
    Physics of Fluids, 1996
    Co-Authors: A L Velikovich, Lee Phillips
    Abstract:

    An analytic small‐amplitude theory of the instability of a plane centered Rarefaction Wave (which has recently been discovered numerically by Yang et al.) is presented. A finite‐difference (FCT) calculation is performed and compares well with the theory. The instability manifests itself as perturbation growth on the Wave’s trailing edge. The asymptotic value approached by the perturbed velocity of the trailing edge is expressed as kδx0a0u∞(M,γ), where k is the perturbation Wave number, δx0 is the constant perturbation amplitude of the leading edge, a0 is the sound speed in the unperturbed gas, and u∞(M,γ) is a dimensionless function that depends on the adiabatic exponent, γ, and the strength of the Rarefaction Wave, M, taken as the ratio of sound speeds behind and ahead of it. This function is essentially determined by the way the perturbed Rarefaction Wave is formed, e.g., by moving a corrugated piston from a gas‐filled space or by interaction of a plane shock Wave with a rippled contact interface betwee...

Linan Li - One of the best experts on this subject based on the ideXlab platform.

M Molenda - One of the best experts on this subject based on the ideXlab platform.

  • development of a Rarefaction Wave at discharge initiation in a storage silo dem simulations
    Particuology, 2018
    Co-Authors: Rafal Kobylka, J Horabik, M Molenda
    Abstract:

    Abstract The generation of a Rarefaction Wave at the initiation of discharge from a storage silo is a phenomenon of scientific and practical interest. The effect, sometimes termed the dynamic pressure switch, may create dangerous pulsations of the storage structure. Owing to the nonlinearity, discontinuity, and heterogeneity of granular systems, the mechanism of generation and propagation of stress Waves is complex and not yet completely understood. The present study conducted discrete element simulations to model the formation and propagation of a Rarefaction Wave in a granular material contained in a silo. Modeling was performed for a flat-bottom cylindrical container with diameter of 0.1 or 0.12 m and height of 0.5 m. The effects of the orifice size and the shape of the initial discharging impulse on the shape and extent of the Rarefaction Wave were examined. Positions, velocities, and forces of particles were recorded every 10 −5  s and used to infer the location of the front of the Rarefaction Wave and loads on construction members. Discharge through the entire bottom of the bin generates a plane Rarefaction Wave that may be followed by a compaction Wave, depending on the discharge rate. Discharge through the orifice generates a spherical Rarefaction Wave that, after reflection from the silo wall, travels up the silo as a sequence of Rarefaction–compaction cycles with constant Wavelength equal to the silo diameter. During the travel of the Wave along the bin height, the Wave amplitude increases with the distance traveled. Simulations confirmed earlier findings of laboratory and numerical (finite element method) experiments and a theoretical approach, estimating the speed of the front of the Rarefaction Wave to range from 70 to 80 m/s and the speed of the tail to range from 20 to 60 m/s.

  • Development of a Rarefaction Wave at discharge initiation in a storage silo—DEM simulations
    Particuology, 2018
    Co-Authors: Rafał Kobyłka, J Horabik, M Molenda
    Abstract:

    Abstract The generation of a Rarefaction Wave at the initiation of discharge from a storage silo is a phenomenon of scientific and practical interest. The effect, sometimes termed the dynamic pressure switch, may create dangerous pulsations of the storage structure. Owing to the nonlinearity, discontinuity, and heterogeneity of granular systems, the mechanism of generation and propagation of stress Waves is complex and not yet completely understood. The present study conducted discrete element simulations to model the formation and propagation of a Rarefaction Wave in a granular material contained in a silo. Modeling was performed for a flat-bottom cylindrical container with diameter of 0.1 or 0.12 m and height of 0.5 m. The effects of the orifice size and the shape of the initial discharging impulse on the shape and extent of the Rarefaction Wave were examined. Positions, velocities, and forces of particles were recorded every 10 −5  s and used to infer the location of the front of the Rarefaction Wave and loads on construction members. Discharge through the entire bottom of the bin generates a plane Rarefaction Wave that may be followed by a compaction Wave, depending on the discharge rate. Discharge through the orifice generates a spherical Rarefaction Wave that, after reflection from the silo wall, travels up the silo as a sequence of Rarefaction–compaction cycles with constant Wavelength equal to the silo diameter. During the travel of the Wave along the bin height, the Wave amplitude increases with the distance traveled. Simulations confirmed earlier findings of laboratory and numerical (finite element method) experiments and a theoretical approach, estimating the speed of the front of the Rarefaction Wave to range from 70 to 80 m/s and the speed of the tail to range from 20 to 60 m/s.

Related terms

Rarefaction Wave - 15 days free trial to Access Experts & Abstracts