Numerical simulation of axisymmetric afterbody flows with jet exhaust

A fifth-order accurate compact difference scheme was used to compute the flow over an axisymmetric afterbody with jet exhaust. The solution was based on the mass-averaged Navier-Stokes equations combined with a two-parameter differential model of turbulence. The computations were performed on a specially generated mesh such that the flow in the exterior and interior of the nozzle could be described simultaneously. Numerical results are presented for various external flow conditions and various chamber pressures.     

Asymptotic behavior of vortices in axisymmetric flow without swirl

We investigate the confinement properties of bounded, nonnegative, compactly supported vortices of axisymmetric incompressible Euler flows without swirl. We show that along one direction of the symmetry axis, its support can grow no faster than O[(t log t)^1/2]. The rate at which it approaches the symmetry axis is also estimated. Together with the result of Maffei–Marchioro on the radial growth rate of the support, it is contained in a slowly expanding tubular region. The techniques of the above‐mentioned authors, Iftimie–Lopes–Nussenzveig and Iftimie–Sideris–Gamblin, are used. Copyright © 2008 John Wiley & Sons, Ltd.     

非线性对流扩散方程的守恒律

利用直接方法研究了非线性对流扩散方程的守恒律,得到了关于非线性对流扩散方程的守恒律乘子性质的一个定理.利用这个定理,可以简化守恒律乘子的确定方程.随后通过对确定方程中的变量函数进行分析,发现在四种情况下乘子的确定方程是可解的.最后解出这些守恒律乘子,利用积分公式法分别得到了四种情况下对应于各个守恒律乘子的守恒律.     

IBVPs for scalar conservation laws with time discontinuous fluxes

The initial boundary value problem for a class of scalar nonautonomous conservation laws in 1 space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity assumptions on the flow are extended to a merely dependence on time. These results ensure, for instance, the well‐posedness of a class of vehicular traffic models with time‐dependent speed limits. A traffic management problem is then shown to admit an optimal solution.     

On the exact solutions and conservation laws to the Benjamin-Ono equation

In the present work, we dealt with exact solutions and conservation laws of the Benjamin-Ono equation. We obtained exact solutions of given equation via the exp$(-\Phi (\xi ))$ method. The obtained solutions are included the hyperbolic functions, trigonometric functions and rational functions. By using the multiplier approach, the conservation laws of the mentioned equation was founded.     

Conservation laws for nonlinear telegraph equations

A complete conservation law classification is given for nonlinear telegraph (NLT) systems with respect to multipliers that are functions of independent and dependent variables. It turns out that a very large class of NLT systems admits four nontrivial local conservation laws. The results of this work are summarized in tables which display all multipliers, fluxes and densities for the corresponding conservation laws. A physical example is considered for possible applications.     

Essential Conservation Laws for Equations with Infinite Symmetries

We consider partial differential equations of variational problems with infinite symmetry groups. We study local conservation laws associated with arbitrary functions of one variable in the group generators. We show that only symmetries with arbitrary functions of dependent variables lead to an infinite number of conservation laws. We also calculate local conservation laws for the potential Zabolotskaya-Khokhlov equation for one of its infinite subgroups.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 190–198, July, 2005.     

Conservation Laws for Single-Server Fluid Networks

We consider single-server fluid networks with feedback and arbitrary input processes. The server has to be scheduled in order to minimize a linear holding cost. This model is the fluid analogue of the so-called Klimov problem. Using the achievable-region approach, we show that the Gittins index rule is optimal in a strong sense: it minimizes the linear holding cost for arbitrary input processes and for all time points t0.     

Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets

The conservation laws for Prandtl’s boundary layer equations for an incompressible fluid governing the flow in radial and two-dimensional jets are investigated. For both radial and two-dimensional jets the partial Lagrangian method is used to derive conservation laws for the system of two differential equations for the velocity components. The Lie point symmetries are calculated for both cases and a symmetry is associated with the conserved vector that is used to establish the conserved quantity for the jet. This associated symmetry is then used to derive the group invariant solution for the system governing the flow in the free jet.     

Conservation laws with a random source

We study the scalar conservation law with a noisy nonlinear source, namely,u _l + f(u)_x = h(u, x, t) + g(u)W(t), whereW(t) is the white noise in the time variable, and we analyse the Cauchy problem for this equation where the initial data are assumed to be deterministic. A method is proposed to construct approximate weak solutions, and we then show that this yields a convergent sequence. This sequence converges to a (pathwise) solution of the Cauchy problem. The equation can be considered as a model of deterministic driven phase transitions with a random perturbation in a system of two constituents. Finally we show some numerical results motivated by two-phase flow in porous media. This research has been supported by VISTA (a research cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap, Statoil) and NAVF (the Norwegian Research Council for Science and the Humanities).     

Local conservation laws,symmetries, and exact solutions for a Kudryashov‐Sinelshchikov equation

In this paper, we consider a Kudryashov‐Sinelshchikov equation that describes pressure waves in a mixture of a liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer between liquid and gas bubbles. We show that this equation is rich in conservation laws. These conservation laws have been found by using the direct method of the multipliers. We apply the Lie group method to derive the symmetries of this equation. Then, by using the optimal system of 1‐dimensional subalgebras we reduce the equation to ordinary differential equations. Finally, some exact wave solutions are obtained by applying the simplest equation method.     

BV solutions for hyperbolic systems of balance laws with relaxation

For hyperbolic systems of balance laws with source manifesting relaxation, it is shown that the Kawashima condition, which yields global classical solutions with smooth initial values near equilibrium, is also instrumental in inducing the existence of global admissible BV solutions, accommodating shocks.     

Continuity in finite time of entropy solutions for nonconvex conservation laws with reaction term

The aim of the paper is to study qualitative properties of entropy solutions to the Cauchy problem for the following reaction-convection equation with nonconvex flux f In particular we prove that under suitable assumptions the solution is continuous for large t.New resultsconcerning the asymptotic behavior of solutions are also given, proving convergence to a suitable combination of traveling profiles with different speeds.     

Regularity of solutions to scalar conservation laws with a force

We prove regularity estimates for entropy solutions to scalar conservation laws with a force. Based on the kinetic form of a scalar conservation law, a new decomposition of entropy solutions is introduced, by means of a decomposition in the velocity variable, adapted to the non-degeneracy properties of the flux function. This allows a finer control of the degeneracy behavior of the flux. In addition, this decomposition allows to make use of the fact that the entropy dissipation measure has locally finite singular moments. Based on these observations, improved regularity estimates for entropy solutions to (forced) scalar conservation laws are obtained.     

Conservation laws for two-phase filtration models

The paper is devoted to investigation of group properties of a one-dimensional model of two-phase filtration in porous medium. Along with the general model, some of its particular cases widely used in oil-field development are discussed. The Buckley–Leverett model is considered in detail as a particular case of the one-dimensional filtration model. This model is constructed under the assumption that filtration is one-dimensional and horizontally directed, the porous medium is homogeneous and incompressible, the filtering fluids are also incompressible. The model of “chromatic fluid” filtration is also investigated. New conservation laws and particular solutions are constructed using symmetries and nonlinear self-adjointness of the system of equations.     

Conservation laws, hierarchy of dynamics and explicit integration of nonholonomic systems

This paper can be regarded as a continuation of our previous work [1, 2] on the hierarchy of the dynamical behavior of nonholonomic systems. We consider different mechanical systems with nonholonomic constraints; in particular, we examine the existence of tensor invariants (laws of conservation) and their connection with the behavior of a system. Considerable attention is given to the possibility of conformally Hamiltonian representation of the equations of motion, which is mainly used for the integration of the considered systems.      

Convergence of Approximate Solutions for Quasilinear Hyperbolic Conservation Laws with Relaxation

In this article the author considers the limiting behavior of quasilinear hyperbolic conservation laws with relaxation, particularly the zero relaxation limit. Our analysis includes the construction of suitably entropy flux pairs to deduce the L∞ estimate of the solutions, and the theory of compensated compactness is then applied to study the convergence of the approximate solutions to its Cauchy problem.     

An adaptive wavelet viscosity method for hyperbolic conservation laws

We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre‐orthogonal spline‐)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least‐squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

Pointwise Stability of Contact Discontinuity for Viscous Conservation Laws with General Perturbations

The large time asymptotic behavior towards viscous contact waves for a class of systems of viscous conservation laws is studied in this paper for general initial perturbations. The high order deviation of the viscous solutions from the leading order ansatz is estimated pointwisely via the approximate Green function approach. The structural constraint on the left eigenvector belonging to the principal linearly degenerate family used in [13 Liu , T. , Xin , Z. ( 1988 ). Pointwise decay to contact discontinuities for systems of viscous conservation laws . Asian J. Math. 1 : 34 – 84 . [Google Scholar]] is removed so that our results hold, in particular, for the one-dimensional compressible Navier–Stokes equations of gas dynamics in both Lagrangian and Eulerian coordinates.