The Riemann problem for non-ideal isentropic compressible two phase flows

We consider the Riemann problem for a five-equation, two-pressure (5E2P) model of non-ideal isentropic compressible gas–liquid two-phase flows. This system is more complex due to the extended thermodynamics model for van der Waals gases, that is, typical real gases for gas phase and Tait׳s equation of state for liquid phase. The overall model is strictly hyperbolic and non-conservative form. We investigate the structure of Riemann problem and construct the solution for it. To construct solution of Riemann problem approximately assuming that all waves corresponding to the genuinely non-linear characteristic fields are rarefaction and then we discuss their properties. Lastly, we discuss numerical examples and study the solution influenced by the van der Waals excluded volume.     

An algorithm for isentropic flow

An efficient algorithm is presented for the solution of the equations of isentropic gas dynamics with a general convex gas law. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only two function evaluations in each computational cell are required. The scheme is applied to a standard test problem in gas dynamics for a polytropic gas.     

Critical time for shock formation in radiative magnetogasdynamics

For the general case of magnetogasdynamics coupled to the radiation field, a differential scheme which is capable of dealing with variable optical depths, leads to a hyperbolic system of equations. To this system the standard techniques for evaluating the critical time of weak discontinuities is applied. In this paper the critical time for radiative magnetoacoustic waves propagating into a constant state is analyzed. Plane waves, spherical waves and cylindrical waves are studied.     

An approximate solution of the Riemann problem for a realisable second-moment turbulent closure

Abstract. 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 linear path to connect states through shocks, approximate jump conditions are derived, and the existence and uniqueness of the one-dimensional Riemann problem solution is then proven. This result enables to construct exact or approximate Riemann-type solvers. An approximate Riemann solver, which is based on Gallou?t's recent proposal is eventually presented. Some computations of shock tube problems are then discussed. Received 2 March 1999 / Accepted 24 August 2000     

Axisymmetric mixed flows in magnetogasdynamics

In contrast with conventional gasdynamics, in magnetogasdynamics there are several types of mixed flows. A detailed study of such plane flows was first made by Kogan [1]. After this, intensive work was done on the magnetogasdynamic mixed flows [2–13], with the plane case being considered in all the studies except [9]. In [9] the equations of the possible mixed flows for the axisymmetric case were obtained in terms of the disturbance velocity components.The axisymmetric mixed flows are studied in detail in the present paper. The exact equations of motion are obtained for the velocity potential and the streamfunction, and the corresponding approximate equations are obtained for all the transitional regimes (transonic, hypercritical, trans-Alfvenic, transonic-trans-Alfvenic). Simple particular solutions are obtained for these approximate equations.For greater generality the entire study is made simultaneously for the plane and axisymmetric cases.The author wishes to thank S. V. Fal'kovich for his interest in the study and for valuable discussions.     

Singular surfaces of order one in magnetogasdynamics

Summary Singular surfaces of order one in Magnetogasdynamics are discussed by applying the compatibility conditions due to Thomas. The propagation of the transverse type of singular surface is discussed at length, and an expression is obtained for the variation of its strength. It is shown that the strength of a plane transverse singular surface remains constant when moving in a uniform medium at rest. For propagation in a non-uniform medium the strength is, however, shown to vary and an expression is derived giving the variation.     

A 3D finite element ALE method using an approximate Riemann solution

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann‐like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann‐like problem. Two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well‐known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

Growth and decay of weak shock waves in magnetogasdynamics

The purpose of the present study is to investigate the problem of the propagation of weak shock waves in an inviscid, electrically conducting fluid under the influence of a magnetic field. The analysis assumes the following two cases: (1) a planar flow with a uniform transverse magnetic field and (2) cylindrically symmetric flow with a uniform axial or varying azimuthal magnetic field. A system of two coupled nonlinear transport equations, governing the strength of a shock wave and the first-order discontinuity induced behind it, are derived that admit a solution that agrees with the classical decay laws for a weak shock. An analytic expression for the determination of the shock formation distance is obtained. How the magnetic field strength, whether axial or azimuthal, influences the shock formation is also assessed.     

Exact solutions to magnetogasdynamics using Lie point symmetries

In the present work, we find some exact solutions to the first order quasilinear hyperbolic system of partial differential equations (PDEs), governing the one dimensional unsteady flow of inviscid and perfectly conducting compressible fluid, subjected to a transverse magnetic field. For this, Lie group analysis is used to identify a finite number of generators that leave the given system of PDEs invariant. Out of these generators, two commuting generators are constructed involving some arbitrary constants. With the help of canonical variables associated with these two generators, the assigned system of PDEs is reduced to an autonomous system whose simple solutions provide nontrivial solutions of the original system. Using this exact solution, we discuss the evolutionary behavior of weak discontinuities.     

The propagation of small disturbances in radiative magnetogasdynamics

Summary The non-linearised equations of flow for a perfectly electrically conducting and thermally radiating inviscid gas are analysed using the differential approximation for a grey gas of arbitrary opacity including effects of radiative flux, pressure and energy density. The speeds of propagation of weak discontinuities are established with oblique magnetic field, together with the jump relations for the derivatives of the field variables. For the special case of one-dimensional flows with planar, cylindrical or spherical symmetry the compatibility conditions on the characteristic surfaces associated with the wavefronts are explicitly determined.     

Shock capturing for steady,supersonic, two-dimensional isentropic flow

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, isentropic flow. The scheme incorporates numerical characteristic decomposition, is shock-capturing by design and incorporates space marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.     

Solution of a Riemann problem for elasticity

This paper describes a numerical algorithm for the Riemann solution for nonlinear elasticity. We assume that the material is hyperelastic, which means that the stress-strain relations are given by the specific internal energy. Our results become more explicit under further assumptions: that the material is isotropic and that the Riemann problem is uniaxial. We assume that any umbilical points lie outside the region of physical relevance. Our main conclusion is that the Riemann solution can be obtained by the iterative solution of functional equations (Godunov iterations) each defined in one- or two-dimensional spaces.Supported in part by AFOSR-88-0025.     

Generalized Riemann problem for gas dynamic combustion

The generalized Riemann problem for gas dynamic combustion in a neighborhood of the origin t > 0 in the (x, t) plane is considered. Under the modified entropy conditions, the unique solutions are constructed, which are the limits of the selfsimilar Zeldovich-von Neumann-Dring (ZND) combustion model. The results show that, for some cases, there are intrinsical differences between the structures of the perturbed Riemann solutions and the corresponding Riemann solutions. Especially, a strong detonation in the...