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32,031
Agglomeration Multigrid for the Three-Dimensional Euler Equations
- AIAA Paper
, 1994
"... A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the threedimensional Euler equations on unstructured grids about complex configurations. It is shown that the agglomeration procedure can be tail ..."
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Cited by 21 (8 self)
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A multigrid procedure that makes use of coarse grids generated by the agglomeration of control volumes is advocated as a practical approach for solving the threedimensional Euler equations on unstructured grids about complex configurations. It is shown that the agglomeration procedure can
Infinite superlinear growth of the gradient for the two-dimensional Euler equation
"... (Communicated by Roger Temam) Abstract. For two-dimensional Euler equation on the torus, we prove that the L ∞ norm of the gradient can grow superlinearly for some infinitely smooth initial data. We also show the exponential growth of the gradient for finite time. 1. Introduction. In this note, we a ..."
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Cited by 11 (1 self)
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(Communicated by Roger Temam) Abstract. For two-dimensional Euler equation on the torus, we prove that the L ∞ norm of the gradient can grow superlinearly for some infinitely smooth initial data. We also show the exponential growth of the gradient for finite time. 1. Introduction. In this note, we
Double exponential growth of the vorticity gradient for the two-dimensional Euler equation
, 2012
"... For two-dimensional Euler equation on the torus, we prove that the L ∞ –norm of the vorticity gradient can grow as double exponential over arbitrarily long but finite time. The method is based on the perturbative analysis around the singular stationary solution studied by Bahouri and Chemin in [1]. ..."
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Cited by 4 (1 self)
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For two-dimensional Euler equation on the torus, we prove that the L ∞ –norm of the vorticity gradient can grow as double exponential over arbitrarily long but finite time. The method is based on the perturbative analysis around the singular stationary solution studied by Bahouri and Chemin in [1].
Evaluation of the Lopatinski determinant for multi-dimensional Euler equations
, 2002
"... The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function, ” for the Euler equations of compressible gas dynamics. We describe two approaches to this problem. In the first we use a change of variables to simplify the computation. In the second method we take adv ..."
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Cited by 6 (4 self)
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The purpose of this appendix is to calculate the Lopatinski determinant, or “stability function, ” for the Euler equations of compressible gas dynamics. We describe two approaches to this problem. In the first we use a change of variables to simplify the computation. In the second method we take
An Inviscid Regularization of the One-Dimensional Euler equations
"... This paper examines an averaging technique in which the nonlinear flux term is ex-panded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in an inviscid regularization of the homentropic Euler equation ..."
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Cited by 1 (0 self)
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equations and Euler equations. The physical motivation for this technique is presented and a general method is derived, which is then applied to the home-ntropic Euler equations and Euler equations. These modified equations are then examined, discovering that they share the conservative properties
Analytic adjoint solutions for the quasi-one-dimensional Euler equations
, 2000
"... The analytic properties of adjoint solutions are examined for the quasi-one-dimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition is requi ..."
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The analytic properties of adjoint solutions are examined for the quasi-one-dimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are continuous with zero gradient at the shock, and that an internal adjoint boundary condition
The three-dimensional Euler equations: Where do we stand?
, 2008
"... The three-dimensional Euler equations have stood for a quarter of a millenium as a challenge to mathematicians and physicists. While much has been discovered, the nature of solutions is still largely a mystery. This paper surveys some of the issues, such as singularity formation, that have cost so m ..."
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Cited by 24 (1 self)
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The three-dimensional Euler equations have stood for a quarter of a millenium as a challenge to mathematicians and physicists. While much has been discovered, the nature of solutions is still largely a mystery. This paper surveys some of the issues, such as singularity formation, that have cost so
Convergence analysis of the Gauss–Seidel Preconditioner for Discretized One Dimensional Euler Equations
- SIAM J. Numer. Anal
, 2003
"... Abstract. We consider the nonlinear system of equations that results from the Van Leer flux vector-splitting discretization of the one dimensional Euler equations. This nonlinear system is linearized at the discrete solution. The main topic of this paper is a convergence analysis of block-Gauss–Seid ..."
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Cited by 2 (1 self)
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Abstract. We consider the nonlinear system of equations that results from the Van Leer flux vector-splitting discretization of the one dimensional Euler equations. This nonlinear system is linearized at the discrete solution. The main topic of this paper is a convergence analysis of block
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