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A note on critical times of 2 × 2 quasilinear hyperbolic systems

Ivan Straškraba (1984)

Aplikace matematiky

In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a 2 × 2 quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.

A note on poroacoustic traveling waves under Darcy's law: Exact solutions

P. M. Jordan, J. K. Fulford (2011)

Applications of Mathematics

A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...

Control of transonic shock positions

Olivier Pironneau (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Control of Transonic Shock Positions

Olivier Pironneau (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .

Description of the multi-dimensional finite volume solver EULER

Pavel Šolín, Karel Segeth (2002)

Applications of Mathematics

This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves. This...

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