scholarly journals Backscattering in complex flows: application of the One-Way Euler equations to Poiseuille flow inside lined duct

2021 ◽  
Author(s):  
Clément Rudel ◽  
Sébastien Pernet ◽  
Jean-Philippe Brazier
Keyword(s):  
Euler Equations ◽  
Poiseuille Flow ◽  
Complex Flows ◽  
The One

scholarly journals On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1039
Author(s):  
Maren Hantke ◽  
Ferdinand Thein
Keyword(s):  
Euler Equations ◽  
Single Phase ◽  
Two Phase Flows ◽  
Two Phase ◽  
First Order ◽  
Engineering Sciences ◽  
The One ◽  
First Order Phase ◽  
Isothermal Euler Equations ◽  
Appl Math

Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point.

scholarly journals Stability of Leapfrog Constant-Coefficients Semi-Implicit Schemes for the Fully Elastic System of Euler Equations: Case with Orography

2005 ◽  
Vol 133 (5) ◽  
pp. 1065-1075 ◽  
Author(s):  
P. Bénard ◽  
J. Mašek ◽  
P. Smolíková
Keyword(s):  
Euler Equations ◽  
Evolution Equations ◽  
Momentum Equation ◽  
Primitive Equations ◽  
Prognostic Variables ◽  
Flat Terrain ◽  
Implicit Schemes ◽  
Constant Coefficients ◽  
The Stability ◽  
The One

Abstract The stability of constant-coefficients semi-implicit schemes for the hydrostatic primitive equations and the fully elastic Euler equations in the presence of explicitly treated thermal residuals has been theoretically examined in the earlier literature, but only for the case of a flat terrain. This paper extends these analyses to a case in which an orography is present, in the shape of a uniform slope. It is shown, with mass-based coordinates, that for the Euler equations, the presence of a slope reduces furthermore the set of the prognostic variables that can be used in the vertical momentum equation to maintain the robustness of the scheme, compared to the case of a flat terrain. The situation appears to be similar for systems cast in mass-based and height-based vertical coordinates. Still for mass-based vertical coordinates, an optimal prognostic variable is proposed and is shown to result in a robustness similar to the one observed for the hydrostatic primitive equations system. The prognostic variables that lead to robust semi-implicit schemes share the property of having cumbersome evolution equations, and an alternative time treatment of some terms is then required to keep the evolution equation reasonably simple. This treatment is shown not to modify substantially the stability of the time scheme. This study finally indicates that with a pertinent choice for the prognostic variables, mass-based vertical coordinates are equally suitable as height-based coordinates for efficiently solving the compressible Euler equations system.

scholarly journals SHOCK FORMATION IN THE COMPRESSIBLE EULER EQUATIONS AND RELATED SYSTEMS

2013 ◽  
Vol 10 (01) ◽  
pp. 149-172 ◽  
Author(s):  
GENG CHEN ◽  
ROBIN YOUNG ◽  
QINGTIAN ZHANG
Keyword(s):  
Euler Equations ◽  
Space Dimension ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Compressible Euler Equations ◽  
Shock Formation ◽  
Compressible Euler ◽  
Systems Of Conservation Laws ◽  
The One ◽  
Special Case

We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry. We establish an L∞ bound for C1 solutions of the one-dimensional (1D) Euler equations, and use this to improve recent shock formation results of the authors. We prove analogous shock formation results for 1D magnetohydrodynamics (MHD) with orthogonal magnetic field, and for compressible flow in a variable area duct, which has as a special case spherically symmetric three-dimensional (3D) flow on the exterior of a ball.

On Numerical Simulations of Complex Flows of Viscoplastic Materials

2000 ◽  
Author(s):  
Paulo R. Souza Mendes ◽  
Mônica F. Naccache ◽  
Harry T. M. Vinagre
Keyword(s):  
Flow Visualization ◽  
Flow Pattern ◽  
Numerical Solutions ◽  
Momentum Balance ◽  
Complex Flows ◽  
Large Expansion ◽  
Liquid Model ◽  
Axisymmetric Channel ◽  
Visualization Experiments ◽  
The One

Abstract The performance of a typical numerical simulation for complex flows of viscoplastic materials was examined. The inertialess flow of viscoplastic materials through an axisymmetric channel formed by an abrupt expansion followed by a contraction was employed with this purpose. Flow visualization experiments were performed with a well characterized Carbopol aqueous solution. Numerical solutions of the mass and momentum balance equations were obtained, using the Generalized Newtonian Liquid model with a biviscosity function. The flow visualization results showed that the flow pattern is essentially Newtonian for large expansion lengths. For smaller expansion lengths, however, flow is observed only in an inner axisymmetric region whose diameter is approximately the same as the one of the inlet and outlet tubes. Outside this region the flow is stagnant, and a slip interface between these two regions seems to occur. The corresponding numerical solution was not capable of predicting the observed flow pattern.

The Simulation of the Linearized Euler Equations by a Second Order Scheme is Possible

2005 ◽  
Vol 4 (1-2) ◽  
pp. 49-68
Author(s):  
R. Abgrall ◽  
M. Ravachol ◽  
S. Marret
Keyword(s):  
Numerical Simulation ◽  
Euler Equations ◽  
Finite Volume ◽  
Unstructured Meshes ◽  
High Order ◽  
Complex Geometries ◽  
Residual Distribution ◽  
Linearized Euler Equations ◽  
Order Scheme ◽  
The One

We are interested in the numerical simulation of acoustic perturbations via the linearized Euler equations using triangle unstructured meshes in complex geometries such as the one around a complete aircraft. It is known that the classical schemes using a finite volume formulation with high order extrapolation of the variables can be very disappointing. In this paper, we show that using an upwind residual distribution formulation, it is possible to simulate such problems, even on truly unstructured meshes. The main focus of the paper is on the propagative properties of the scheme.

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