An approximate solution of the Riemann problem associated with a realisable and objective turbulent second-moment closure, which is valid for compressible flows, is examined. The main features of the continuous model are first recalled. An entropy inequality is exhibited, and the structure of waves associated with the non-conservative hyperbolic convective system is briefly described. Using a l...

In this work, two extensiosn of our previous work are proposed for the simulation of full-Mach-range cavitating flow with sharp interface model. These extensions are: a new interface-interaction solver, which includes a new HLLC Riemann solver suitable for both strong and weak interface interaction with general EOS, and a simple phase-change model which assumes that the phase change is in therm...

We present a theoretical solution for the Riemann problem for the five-equation two-phase non-conservative model of Saurel and Abgrall. This solution is then utilized in the construction of upwind non-conservative methods to solve the general initial-boundary value problem for the two-phase flow model in non-conservative form. The basic upwind scheme constructed is the non-conservative analogue...

In this paper, we present recent results in integral inequality theory. Our results are based on thefractional integration in the sense of Riemann-Liouville

Shock wave theory was studied in literature by many authors. This article presents a survey with references about various topics related to shock waves: Hyperbolic conservation laws, Well-posedness theory, Compactness theory, Shock and reaction-di¤usion wave, The CJ and ZND theory, Existence of detonation in Majda’s model, Premixed laminar ‡ame, Multidimensional gas ‡ows, Multidimensional Riema...

We study a Riemann problem for the unsteady transonic small disturbance equations that results in a diverging rarefaction problem. The self-similar reduction leads to a boundary value problem with equations that change type (hyperbolic-elliptic) and a sonic line that is a free boundary. We summarize the principal ideas and present the main features of the problem. The flow in the hyperbolic par...

In this note, we consider the Riemann problem for a twodimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover...

The paper studies a class of conservation law models for traffic flow on a family of roads, near a junction. A Riemann Solver is constructed, where the incoming and outgoing fluxes depend Hölder continuously on the traffic density and on the drivers’ turning preferences. However, various examples show that, if junction conditions are assigned in terms of Riemann Solvers, then the Cauchy problem...

Extended thermodynamics derives dissipative, hyperbolic field equations for monatomic gases. One example is the system of the 13-field-case, which is a dissipative extension of the Euler equations. In this paper the system is investigated by solving a Riemann problem. Additionally some model equations are introduced so as to discuss the main properties in a transparent manner. There arises an i...

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...