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Communications on Applied Mathematics and Computation 2020年第3期2卷 341-368页

作者： rémi abgrall Institüt für Mathematik Universität ZürichWinterhurerstrasse 1908057ZurichSwitzerland

In this paper,we discuss the notion of discrete conservation for hyperbolic conservation *** introduce what we call fluctuation splitting schemes(or residual distribution,also rDS)and show through several examples how these schemes lead to new *** particular,we show that most,if not all,known schemes can be rephrased in flux form and also how to satisfy additional conservation *** 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 ***[26],roe mentioned the Hermes project and the role of Dassault *** 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 *** helped me a lot in understanding the notion of *** 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.

关键词： Hyperbolic problems Local conservation residual distribution

Neural Network-Based Limiter with Transfer Learning

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Communications on Applied Mathematics and Computation 2023年第2期5卷 532-572页

作者： rémi abgrall Maria Han Veiga University of Zurich ZurichSwitzerland University of michigan Ann ArborUSA

recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et *** A machine learning approach for detect-ing shocks with high-order hydrodynamic *** *** J Comput Phys 367:166-191.,2018;Veiga et *** European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,***.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a runge-Kutta discontinuous Galer-kin(rKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard ***,we describe a strategy to transfer the shock-indicator to a residual distribution(rD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an rD scheme to an rKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured *** report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both rKDG and rD schemes.

关键词： Limiters Neural networks Transfer learning Domain adaptation

An Arbitrarily High Order and Asymptotic Preserving Kinetic Scheme in Compressible Fluid Dynamic

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Communications on Applied Mathematics and Computation 2024年第2期6卷 963-991页

作者： remi abgrall Fatemeh Nassajian Mojarrad Institute of Mathematics University of ZurichWinterthurerstrasse 190CH 8057 ZürichSwitzerland

We present a class of arbitrarily high order fully explicit kinetic numerical methods in compressible fluid dynamics,both in time and space,which include the relaxation schemes by Jin and *** methods can use the CFL number larger or equal to unity on regular Cartesian meshes for the multi-dimensional *** kinetic models depend on a small parameter that can be seen as a"Knudsen"*** method is asymptotic preserving in this Knudsen ***,the computational costs of the method are of the same order of a fully explicit *** work is the extension of abgrall et al.(2022)[3]to multidimensional *** have assessed our method on several problems for two-dimensional scalar problems and Euler equations and the scheme has proven to be robust and to achieve the theoretically predicted high order of accuracy on smooth solutions.

关键词： Kinetic scheme Compressible fluid dynamics High order methods Explicit schemes Asymptotic preserving Defect correction method

Preface to the Focused Issue in Honor of Professor Philip roe on the Occasion of His 80th Birthday

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Communications on Applied Mathematics and Computation 2020年第3期2卷 319-320页

作者： rémi abgrall Jennifer K.ryan Chi-Wang Shu Institüt für Mathematik Universität ZürichWinterhurerstrasse 1908057ZurichSwitzerland Department of Applied Mathematics and Statistics Colorado School of MinesGoldenCO80401USA Division of Applied Mathematics Brown UniversityProvidenceRI02912USA

On July 3-4,2018,an international workshop was organised at the University of Cambridge,by ***,to mark the 80th anniversary of a young scientist,Philip ***'s scientific achievements are numerous,and it is quite difficult to adequately address his accomplishments in a short *** began his journey at Cambridge,first for his Bachelor's degree and then obtaining his Master's degree in *** left for the royal Aircraft Establishment(rAE)between 1962 to 1984 to work as an *** was a period of adventure,and the design of mature CFD codes for solving the Euler equations was far from being *** the Lax-Wendroff theorem was known(published in 1960),as for many novelties,it had taken some time before it became a gold *** the rAE,Phil was assigned by his manager to work in a direction that eventually led to roe's riemann solver and *** method is now standard in every specialised textbook,but the jump from generalizing the Murman scheme for Euler equations to what is now commonly known as the roe flux is far from *** roe relates this adventure,and others,in his"scientific autobiography",one of the papers of this focused issue.

关键词： eventually accomplishment assigned

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Preface

Communications on Applied Mathematics and Computation 2024年第3期6卷 1519-1520页

作者： W.Boscheri F.Chinesta r.Loubere S.mishra G.Puppo M.ricchiuto C.-W.Shu Laboratoire de Mathématiques UMr 5127 CNrS UniversitéSavoie Mont Blanc73376 Le Bourget-du-LacFrance ESI Group Chair PIMM Lab Arts et Métiers Institute of Technology151 Boulevard de l’HôpitalF-75013 ParisFrance Institut de Mathématiques de Bordeaux(IMB)UMr 5251 CNrS Universitéde Bordeaux351 cours de la Libération33405 Talence CedexFrance Seminar for Applied Mathematics Department of Mathematicsand ETH AI CenterETH ZurichRämistrasse 1018092 ZurichSwitzerland Dipartimento di Matematica Sapienza Universitàdi RomaP.le Aldo Moro 500185 RomeItaly INrIA Universitéde BordeauxCNRSBordeaux INPIMB UMR 5251200 Avenue de la Vieille Tour33405 Talence CedexFrance Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

This focused issue of the Communications on Applied Mathematics and Computation is in Honour of Prof.rémi abgrall on the Occasion of His 61th Birthday.rémi abgrall has been a student in mathematics(1981–1985)of Ecole Normale Supérieure de Saint Cloud(now part of ENS Lyon).After his studies in pure mathematics,he changed orientation toﬂuid *** did his PhD at the Laboratoire de Météorologie Dynamique(LMD)at Ecole Normale Supérieure under the supervision of Claude *** graduated in December 1987 with a thesis on a semi-Lagrangian model of 2D turbulence,refereed by Olivier Pironneau and Marcel Lesieur.

关键词： has turbulence Les