UNIFORM FORMULA FOR THE RIEMANN SOLUTIONS OF A SCALAR COMBUSTION MODEL

In this paper, we construct a uniform formula for the Riemann solutions of the simplified Chapman-Jouguet model. Firstly, we define a new functional, and then, we obtain that the Riemann solutions can be expressed by the maximum value point of this functional,while Riemann solutions may contain some of strong detonation waves, Chapman-Jouguet detonation waves and contact discontinuities. Finally, Chapman-Jouguet deflagration waves are also discussed.

EXISTENCE AND NONEXISTENCE OF GLOBAL CONTINUOUS SOLUTIONS TO RIEMANN PROBLEM FOR DAMPED P-SYSTEM

In this paper, we extend the result in [16] to general p(v). We prove that, under condition (M), when P greater-than-or-equal-to 3/2, where P=pp triple overdot/p2, there exists a unique global continuous solution to the Riemann problem (E), (R), whose structure is similar to the local solution. When 1 < P* less-than-or-equal-to P* < 5/4, or P* = P* = 5/4, or 5 < P* less-than-or-equal-to P* < 3/2 where P*-inf/v P and P* = sup/v P for all v under consideration, if at least one of the initial centered rarefaction waves is sufficiently strong, then the solution must be breakdown in a finite time.

A NOTE ON THE RIEMANN PROBLEM TO HYPERBOLIC CONSERVATION LAWS

This paper is a extension of [1], [3]. By the method in [1], the authors prove the global existence of the solutions of the Riemann problem for a class of 2 × 2 nonstrictly hyperbolic conservation laws.

Numerical Simulation of Water Mitigation Effects on Shock Wave with SPH Method

The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numerical results with the analytical solution indicated that the modified SPH method has more advantages than the traditional SPH method. Using the modified SPH algorithm, a series of one-dimensional planar wave propagation problems were investigated, focusing on the influence of the air-gap between the high-pressure air and water and the thickness of water. The numerical results showed that water mitigation effect is significant. Up to 60% shock wave pressure reduction could be achieved with the existence of water, and the shape of shock wave was also changed greatly. It is seemly that the small air-gap between the high-pressure air and water has more influence on water mitigation effect.

A HYPERBOLIC SYSTEM OF CONSERVATION LAWS FOR FLUID FLOWS THROUGH COMPLIANT AXISYMMETRIC VESSELS

We are concerned with the derivation and analysis of one-dimensional hyperbolic systems of conservation laws modelling fluid flows such as the blood flow through compliant axisyminetric vessels. Early models derived are nonconservative and/or nonho- mogeneous with measure source terms, which are endowed with infinitely many Riemann solutions for some Riemann data. In this paper, we derive a one-dimensional hyperbolic system that is conservative and homogeneous. Moreover, there exists a unique global Riemann solution for the Riemann problem for two vessels with arbitrarily large Riemann data, under a natural stability entropy criterion. The Riemann solutions may consist of four waves for some cases. The system can also be written as a 3 × 3 system for which strict hyperbolicity fails and the standing waves can be regarded as the contact discontinuities corresponding to the second family with zero eigenvalue.

Global Entropy Solutions of the Cauchy Problem for Nonhomogeneous Relativistic Euler System

We analyze the 2 × 2 nonhomogeneous relativistic Euler equations for perfect fluids in special relativity. We impose appropriate conditions on the lower order source terms and establish the existence of global entropy solutions of the Cauchy problem under these conditions.

Bcklund Transformations and Solutions of a Generalized Kadomtsev-Petviashvili Equation

In this paper, the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials. The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function, respectively. And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution. In the end, the bilinear Backlund transformations are derived.

Dark Soliton Solutions of Space-Time Fractional Sharma–Tasso–Olver and Potential Kadomtsev–Petviashvili Equations

Dark soliton solutions for space-time fractional Sharma–Tasso–Olver and space-time fractional potential Kadomtsev–Petviashvili equations are determined by using the properties of modified Riemann–Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma–Tasso–Olver equation as only one solution for the potential Kadomtsev–Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

A Contact SPH Method with High-Order Limiters for Simulation of Inviscid Compressible Flows

In this paper,we study a class of contact smoothed particle hydrodynamics(SPH)by introducing Riemann solvers and using high-order limiters.In particular,a promising concept ofWENO interpolation as limiter is presented in the reconstruction process.The physical values relating interactional particles used as the initial values of the Riemann problemcan be reconstructed by the Taylor series expansion.The contact solvers of the Riemann problem at contact points are incorporated in SPH approximations.In order to keep the fluid density at the wall rows to be consistent with that of the inner fluid wall boundaries,several lines of dummy particles are placed outside of the solid walls,which are assigned according to the initial configuration.At last,the method is applied to compressible flows with sharp discontinuities such as the collision of two strong shocks and the interaction of two blast waves and so on.The numerical results indicate that the method is capable of handling sharp discontinuity and efficiently reducing unphysical oscillations.