Riemann-Problem and Level-Set Approaches for Homentropic Two-Fluid Flow Computations B. Koren,∗ M. R. Lewis,∗,1 E. H. van Brummelen,∗,2 and B. van Leer†,1 ∗CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands; and †University of Michigan, Department of Aerospace Engineering, Ann Arbor, Michigan 48109-2140 E-mail: [email protected], [email protected], [email protected], and br...

where t>0, o o < x < o o , U(t, x)=(u(t, x), v(t, x)), and the function F(U)= (f(u, v), g(u, v)) is smooth. GLIMM [2] has proved existence of a weak solution provided that the variation of the initial data Uo(x) is small. GLIMM & LAX [3] then improved this result by requiring that the oscillation of Uo(x) be small. SMOLLER [7] has proved the existence of a weak solution provided that Uo(x ) is ...

The inverse scattering problem on half-axis, in other words, in the spherically symmetric case, consists of finding the unknown potential from a suitable class from the scattering data S. The other problem of practical interest is to find this potential from the spectral data dρ(λ). In the literature there are recovery procedures for finding the potential from the spectral or from the scatterin...

In this paper we first briefly review the semi-analytical method [20] for solving the Derivative Riemann Problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it to hyperbolic systems for which the Riemann problem solution is not available. As an application example we implement the new derivative Riemann solver in the high-order finite-volume ADER advection...

Consider a junction with n incoming and m outgoing roads. Along each road, the flow of traffic is described through the continuum model displaying phase transitions introduced in [5]. This note provides a Riemann solver for the resulting Riemann problem at the junction. 2000 Mathematics Subject Classification: 35L65, 90B10.

This paper studies many fundamental aspects of a newly proposed multi-class traffic flow model. For the first time it presents a complete discussion on the hyperbolicity of the system; and based upon this, the admissible waves of the Riemann problem are deeply investigated. Many important conclusions are made in discussions, and the related physical meanings are interpreted. For the confirmatio...

We consider the complete Euler system describing the time evolution of an inviscid nonisothermal gas. We show that the rarefaction wave solutions of the 1D Riemann problem are stable, in particular unique, in the class of all bounded weak solutions to the associated multiD problem. This may be seen as a counterpart of the non-uniqueness results of physically admissible solutions emanating from ...

We analize the structure of the general solution of the Riemann problem for a striclty hyperbolic system of conservation laws whose characteristic elds are neither genuinely non-linear nor linearly degenerate in the sense of Lax.