1,722,935 research outputs found
Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes
Get PDFIn [1] is proposed a simplified DeC method, that, when combined with the
residual distribution (RD) framework, allows to construct a high order,
explicit FE scheme with continuous approximation avoiding the inversion of the
mass matrix for hyperbolic problems. In this paper, we close some open gaps in
the context of deferred correction (DeC) and their application within the RD
framework. First, we demonstrate the connection between the DeC schemes and the
RK methods. With this knowledge, DeC can be rewritten as a convex combination
of explicit Euler steps, showing the connection to the strong stability
preserving (SSP) framework. Then, we can apply the relaxation approach
introduced in [2] and construct entropy conservative/dissipative DeC (RDeC)
methods, using the entropy correction function proposed in [3].
[1] R. Abgrall. High order schemes for hyperbolic problems using globally
continuous approximation and avoiding mass matrices. Journal of Scientific
Computing, 73(2):461--494, Dec 2017.
[2] D. Ketcheson. Relaxation Runge--Kutta methods: Conservation and stability
for inner-product norms. SIAM Journal on Numerical Analysis, 57(6):2850--2870,
2019.
[3] R. Abgrall. A general framework to construct schemes satisfying
additional conservation relations. application to entropy conservative and
entropy dissipative schemes. Journal of Computational Physics, 372:640--666,
2018
Aspects du Morbihan... Photographies de l'auteur / Raymond Abgrall
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Les croix et les calvaires du Finistère
No full textAbgrall . Les croix et les calvaires du Finistère. In: Bulletin Monumental, tome 66, année 1902. pp. 176-209
The notion of conservation for residual distribution schemes (or fluctuation splitting schemes), with some applications
No full textIn this paper, we discuss the notion of discrete conservation for hyperbolic conservation laws. We introduce what we call fluctuation splitting schemes (or residual distribution, also RDS) and show through several examples how these schemes lead to new developments. In particular, we show that most, if not all, known schemes can be rephrased in flux form and also how to satisfy additional conservation laws. This review paper is built on Abgrall et al. (Computers and Fluids 169:10–22, 2018), Abgrall and Tokareva (SIAM SISC 39(5):A2345–A2364, 2017), Abgrall (J Sci Comput 73:461–494, 2017), Abgrall (Methods Appl Math 18(3):327–351, 2018a) and Abgrall (J Comput Phys 372, 640–666, 2018b). This paper is also a direct consequence of the work of Roe, in particular Deconinck et al. (Comput Fluids 22(2/3):215–222, 1993) and Roe (J Comput Phys 43:357–372, 1981) where the notion of conservation was first introduced. In [26], Roe mentioned the Hermes project and the role of Dassault Aviation. Bruno Stoufflet, Vice President R&D and advanced business of this company, proposed me to have a detailed look at Deconinck et al. (Comput Fluids 22(2/3):215–222, 1993). To be honest, at the time, I did not understand anything, and this was the case for several years. I was lucky to work with Katherine Mer, who at the time was a postdoc, and is now research engineer at CEA. She helped me a lot in understanding the notion of conservation. The present contribution can be seen as the result of my understanding after many years of playing around with the notion of residual distribution schemes (or fluctuation-splitting schemes) introduced by Roe
Jean-Marie Abgrall, La mécanique des sectes (coll. Documents Payot). 1996
No full textWeber Philippe. Jean-Marie Abgrall, La mécanique des sectes (coll. Documents Payot). 1996. In: Revue théologique de Louvain, 28ᵉ année, fasc. 3, 1997. pp. 411-412
Jean-Marie Abgrall, La mécanique des sectes (coll. Documents Payot). 1996
No full textWeber Philippe. Jean-Marie Abgrall, La mécanique des sectes (coll. Documents Payot). 1996. In: Revue théologique de Louvain, 28ᵉ année, fasc. 3, 1997. pp. 411-412
Architecture bretonne : Étude des Monuments du diocèse de Quimper, par l'abbé J.-M. Abgrall
No full textJordan Edouard. Architecture bretonne : Étude des Monuments du diocèse de Quimper, par l'abbé J.-M. Abgrall. In: Annales de Bretagne. Tome 21, numéro 2, 1905. pp. 243-244
Some Failures of Riemann Solvers
No full textIn this small chapter, we review a few problems of classical Riemann solvers for the Euler equations. They are all related to the existence of linearly degenerate fields in this system and the averaging procedure of finite volume methods. © 2017 Elsevier B.V
An ALE formulation for explicit Runge-Kutta Residual Distribution
No full textIn this paper we consider the solution of hyperbolic conservation laws on moving meshes by means of an Arbitrary Lagrangian Eulerian (ALE) formulation. In particular we propose an ALE framework for the genuinely explicit residual distribution schemes of (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). The discretizations obtained are thoroughly tested on a large number of benchmarks.Dans ce travail on considére la resolution de lois de conservation sur maillages mobiles par une formulation Arbitrary Lagrangian Eulerian (ALE). On propose en particulier un formalisme ALE pour les schémas RD explicites de (Ricchiuto and Abgrall {\it J.Comput.Phys} 229, 2010). Les schémas ainsi obtenus sont testés sur des nombreux benchmarks
A simple construction of very high order non oscillatory compact schemes on unstructured meshes.
Get PDFInternational audienceIn \cite{abgrall-roe} have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following \cite{abgrall}, we develop a systematic way of constructing very high order non oscillatory schemes for such meshes. Applications to scalar and systems problems are given
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