首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 93 毫秒
1.
The Riemann problems for the Euler system of conservation laws of energy and momentum in special relativity as pressure vanishes are considered. The Riemann solutions for the pressureless relativistic Euler equations are obtained constructively. There are two kinds of solutions, the one involves delta shock wave and the other involves vacuum. The authors prove that these two kinds of solutions are the limits of the solutions as pressure vanishes in the Euler system of conservation laws of energy and momentum in special relativity.  相似文献   

2.
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models.Where well posedness was known only locally in time,it is here extended to all of R +.The results on the stability with respect to the equations are improved.Moreover,here the case of several populations is considered,obtaining the well posedness of systems of multi-D non-local conservation laws.The basic analytical tools are provided by the classical Kruˇzkov theory of scalar conservation laws in several space dimensions.  相似文献   

3.
<正>The history of hyperbolic system of conservation laws can date back to the eighteenth century, after several works of the natural philosophers, most notably L. Euler. The compressible Euler system, consisting of mass, momentum and energy in the divergence form, is the prototypical model of the hyperbolic system of conservation laws, and its main feature is the shock formation in a finite time no matter how the initial values smooth. This poses huge challenges in the mathematical analysi...  相似文献   

4.
In this paper we further explore and apply our recent anti-diffusive flux corrected highorder finite difference WENO schemes for conservation laws [18] to compute the Saint-Venant system of shallow water equations with pollutant propagation, which is describedby a transport equation. The motivation is that the high order anti-diffusive WENOscheme for conservation laws produces sharp resolution of contact discontinuities whilekeeping high order accuracy for the approximation in the smooth region of the solution.The application of the anti-diffusive high order WENO scheme to the Saint-Venant systemof shallow water equations with transport of pollutant achieves high resolution  相似文献   

5.
This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations (PDE) at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively. The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers' equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative.  相似文献   

6.
A multisymplectic Fourier pseudo-spectral scheme,which exactly preserves the discrete multisymplectic conservation law,is presented to solve the Klein-Gordon-Schrdinger equations.The scheme is of spectral accuracy in space and of second order in time.The scheme preserves the discrete multisymplectic conservation law and the charge conservation law.Moreover,the residuals of some other conservation laws are derived for the geometric numerical integrator.Extensive numerical simulations illustrate the numerical behavior of the multisymplectic scheme,and demonstrate the correctness of the theoretical analysis.  相似文献   

7.
We study the long time formation of rarefaction waves appearing in balance laws by means of singular perturbation methods. The balance laws are non standard because they contain a variable u that appears only in the flux terms. We present a concrete example occurring in flow of steam, nitrogen and water in porous media and an abstract example for a class of systems of three equations. In the concrete example the zero-order equations resulting from the expansion yield a type of conservation law system called compositional model in Petroleum Engineering. In this work we show how compositional models originate from physically more fundamental systems of balance laws. Under appropriate conditions, we prove that certain solutions of the system of balance laws decay with time to rarefaction wave solutions in the compositional model originating from the system of balance laws.  相似文献   

8.
The problem of the presence of Cantor part in the derivative of a solution to a hyperbolic system of conservation laws is considered.An overview of the techniques involved in the proof is given,and a collection of related problems concludes the paper.  相似文献   

9.
§ 1. Introduction The Riemann problem is the most basic problem for both analytical theory and numerical computation of nonlinear hyperbolic conservation laws. B. Riemann suggested and solved it for one dimensional isentropic flow in 1860. A lot of work have been done for 1-D case since 1940's. For 2-D scalar conservation law, it has been solved by Wagner and Zhang and Zheng. For 2-D system of Euler equations in gas dynamios, after some demonstration and analysis with characteristic method in both physics and phase spaces a set of conjectures on the structure of solutions have been formulated by Zhang and Zheng. To approach the proof of the conjectures, we consider a 2×2 system first. In the present paper we discuss the following system:  相似文献   

10.
Considering the integrable properties for the coupled equations, the variable-coefficient N-coupled nonlinear Schrdinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Bcklund transformation for such a coupled system denoting in the Γ functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.  相似文献   

11.
Recent years the modify ghost fluid method (MGFM) and the real ghost fluid method (RGFM) based on Riemann problem have been developed for multimedium compressible flows. According to authors, these methods have only been used with the level set technique to track the interface. In this paper, we combine the MCFM and the RGFM respectively with front tracking method, for which the fluid interfaces are explicitly tracked by connected points. The method is tested with some one-dimensional problems, and its applicability is also studied. Furthermore, in order to capture the interface more accurately, especially for strong shock impacting on interface, a shock monitor is proposed to determine the initial states of the Riemann problem. The present method is applied to various one- dimensional problems involving strong shock-interface interaction. An extension of the present method to two dimension is also introduced and preliminary results are given.  相似文献   

12.
We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.  相似文献   

13.
We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain with the pressure law p(e,θ) - qθ+eln^α(1+e). For the heat flux q ~ -(1+θ^m) △θwe show the existence of a weak solution provided α〉max{1,1/m}, m 〉0. This improves the recent result from [1].  相似文献   

14.
In this paper we prove local well-posedness in critical Besov spaces for the full compressible MHD equations in R^N, N≥ 2, under the assumptions that the initialdensity is bounded away from zero. The proof relies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.  相似文献   

15.
In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβwith β≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.  相似文献   

16.
We study the Green's function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magnetohydrodynamics. More generally, we consider general systems under the basic Kawashima- Shizuta type of conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves pertaining to different characteristic families. The second result is on the continuous differentiability of the Green's function with respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors.  相似文献   

17.
This paper deals with the finite element approximation of an integro-differential equation related with Riemann zeta-function.  相似文献   

18.
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n(n ≥ 3) with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.  相似文献   

19.
In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of ...  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号