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Thursday, July 30, 2020 | History

3 edition of On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws found in the catalog.

On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws

Andrzej Hanyga

# On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws

## by Andrzej Hanyga

Written in English

Subjects:
• Shock waves.,
• Conservation laws (Mathematics),
• Differential equations, Hyperbolic -- Numerical solutions.,
• Riemann-Hilbert problems.

• Edition Notes

Classifications The Physical Object Other titles On the solution to the Riemann problem ... Statement Andrzej Hanyga. Series Publications of the Institute of Geophysics ;, A-1(98), Publications of the Institute of Geophysics ;, 98., Publications of the Institute of Geophysics., 1. LC Classifications QA927 .H18 Pagination 123 p. ; Number of Pages 123 Open Library OL3899496M LC Control Number 81461584

The solution of the Riemann problem involves discontinuous changes in characteristic speeds due to transitions from elastic to plastic response. Illustrations are presented, in both state-space and self-similar coordinates, of the variety of possible solutions to the Riemann problem for possible use with numerical ://   We are concerned with the vanishing viscosity limit of the 2D compressible micropolar equations to the Riemann solution of the 2D Euler equations which admit a planar rarefaction wave. In this article, the key point of the analysis is to introduce the hyperbolic wave, which helps us obtain the desired uniform estimates with respect to the viscosities. Moreover, the proper combining of rotation

Hyperbolic Problems: Theory, Numerics, Applications. Hyperbolic Problems: Theory, Numerics, Applications pp | Cite as. Numerical Aspects of Parabolic Regularization for Resonant Hyperbolic Balance Laws. Authors On the solution to the Riemann problem for the compressible duct flow, SIAM J. Appl. Math. 64(3), This is presently an active area. To set the stage, we begin by solving a classic problem. We prove that the solution of the scalar equation $$u_t + f(u)_x + g(u)_y = 0$$ with Riemann initial data of the form $$u(0,x,y)=u_0(\theta) (0\leq \theta \leq 2 \pi)$$ remains smooth outside a circle with center at the origin in the self-similar plane

problem for nonlinear hyperbolic systems of conservation laws in one space dimension. We consider systems which are strictly hyperbolic and genuinely nonlinear in the sense of Lax [lo]. We present the method here in the setting of systems of two conservation laws, Ut + G(U), F 0, - ?sequence=1.   problem in the entire ﬁeld of conservation laws.”∗ 2 Scalar Conservation Laws The study of two-dimensional Riemann problems of scalar conservation laws was dated back to Guckenheimer in [35]. In , he constructed a Riemann solution for ut + u2 2 x + u3 3 y = 0 () O x y u = 0 u = 1 u = −1 (a) Gukenheimer initial data ξ η S R u ~lijiequan/publications/

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### On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws by Andrzej Hanyga Download PDF EPUB FB2

A new approach to obtaining the approximate solution to the Riemann problem stated for the non-conservative hyperbolic system of quasi-linear partial differential equations has been proposed. The solution to be derived with the method proposed takes into account the complete set of waves associated with the eigenvalues of the system Jacobian   The global Riemann problem for a nonstrictly hyperbolic system of conservation laws modeling polymer flooding is solved.

In particular, the system contains a   In the present paper, the Riemann Problem for a quasilinear hyperbolic system of equations, governing the one dimensional unsteady flow of an inviscid and perfectly conducting gas, subjected to transverse magnetic field, is solved analytically without any restriction on the initial :// E.F.

Toro, in Handbook of Numerical Analysis, 8 Concluding Remarks. The Riemann problem has become a broad research theme in computational science, of which a very succinct account has been given in this chapter.

To start with, some basic definitions and simple examples of Riemann problems have been given. Then, the exact solution of the Riemann problem for the compressible Euler We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class.

This systems it is a simplification of a recently propose system of five   However, in the case of a discontinuous bottom, the application of the Riemann problem can be problematic due to the nonuniqueness of the solution.

This paper presents a possible solution to this problem. The peculiarity of the Riemann problem, lies in the fact that for x = 0 there is a bottom discontinuity and derivative ∂ b / ∂ x in ://   ever the initial Riemann data give rise to a self-similar solution consisting of one admissible shock and one rarefaction wave and are not too far from lying on a simple shock wave, the problem admits also in nitely many admissible weak solutions.

1 Introduction In this note we consider the Euler system of isentropic gas dynamics in two space   () Two dimensional Riemann problem for a 2 × 2 system of hyperbolic conservation laws involving three constant states. Applied Mathematics and Computation() Fine structures for the solutions of the two-dimensional Riemann problems by high-order WENO :// from book Upwind and High-Resolution Schemes (pp) On Upstream Differencing and Godunov-type Schemes for Hyperbolic Conservation Laws Chapter January with Reads   Roe (, J.

Comput. Phys. 43, ). The solver is based on a multistate Riemann problem and is suitable for arbitrary triangular grids or any other ﬁnite volume tes- Consider an integral form of a system of hyperbolic conservation laws d dt Z A udSC Z 0 t/is the solution of the 3-state Riemann problem with the initial data from the   The role of the Riemann problem in the numerical solution of hyperbolic conservation laws can be traced back to the work of Godunov (Godunov, ).

He proposed a method of approximation based on the following steps: Approximate the solution by a piecewise-constant function, e.g.

by averaging it over a set of intervals (or grid cells)   The Cauchy problem for the 2 X 2 system of oil-polymer equations () has a global weak solution for arbitrary initial data of bounded variation in z and c.

Our method involves a detailed study of the Riemann problem solutions to system (), and so ~temple/!!!PubsForWeb/   the Riemann problem for systems of two hyperbolic conservation laws in one space variable. Our main assumptions are that the system is strictly hyperbolic and genuinely nonlinear.

We also require that the system satisfy standard conditions on the second Frtchet derivatives, and The analytical solution for the Riemann problem can be computed using the method established by Gottlieb and Groth [4]. This procedure has been programmed in the form of a Gui-Qiang Chen, Dehua Wang, in Handbook of Mathematical Fluid Dynamics, The multidimensional Riemann problem.

The multidimensional Riemann problem is very important, since it serves as a building block and standard test model of mathematical theories and numerical methods for solving nonlinear systems of conservation laws, especially the Euler equations for compressible fluids,   The Riemann problem for two-dimensional gas dynamics with isentropic or polytropic gas is considered.

The initial data is constant in each quadrant and chosen so that only a rarefaction wave, shock wave, or slip line connects two neighboring constant initial ://   () the riemann problem for a two-dimensional hyperbolic system of conservation laws with non-classical shock waves.

Acta Mathematica Scientia() On the numerical solution of non-linear reservoir flow models with :// Lecture 2 - On the geometric solutions of the Riemann problem for one class of systems of conservation laws.

Speaker: Vladimir Palin, Moscow State University Time: Beijing time ( Moscow time) Abstract: We consider the Riemann problem for a system of conservation    Conservation laws These notes concern the solution of hyperbolic systems of conservation laws.

These are time-dependent systems of partial differential equations (usually nonlinear) with a par-ticularly simple structure. In one space dimension the equations take the form a u(x, t) tionally, the Riemann problem for a system of conservation laws in two independent variables x and t is the initial-value problem (IVP) for the system with initial con-ditions consisting of two constant states separated by a discontinuity at the origin x = 0 (for background see, for example, Godunov () and Toro ()).

?doi=&rep=rep1&type=pdf. The Riemann and Cauchy problems are solved globally for a singular system of n hyperbolic conservation laws. The system, which arises in the study of oil-reservoir simulation, has only two wave   structure of solutions to the Riemann problem () and ().

In fact, the concept of Dirac delta function was rst introduced into the classical weak solution of hyperbolic conservation laws by Korchinski [11] in when he considered the Riemann problem for the system u t+ (1 2 u2) x= 0; v t+ (1 2 uv) x= 0; ()  This dissertation is concerned with the Riemann problem for 2 × 2 hy-perbolic systems of conservation laws in one space variable.

The Riemann problem for 2×2 systems of conservation laws in one space variable, ut +f(u,v)x = 0, vt +g(u,v)x = 0, t > 0, −∞