Adaptive-mesh zoning by the equipotential method

Winslow, A.M.

doi:10.2172/6227449

Cited by 82 publications

(54 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…on the interior of the domain, following the practice in [38]. In our numerical simulations, this simple mesh movement scheme performs well, allowing fairly large grid deformations without leading to ill-conditioned elements or adding error to the simulations, but of course many more sophisticated mesh movement schemes can be considered (see [19]).…”

Section: A Fully Coupled Model Our Incompressible Linear Visco-elastmentioning

confidence: 93%

Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction

Barker¹,

Cai²

2010

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

Abstract. We introduce and study numerically a two-level Schwarz preconditioner for NewtonKrylov methods for fluid-structure interaction, with special consideration of the application area of simulating blood flow. Our approach monolithically couples the fluid to the structure on both fine and coarse grids and in the subdomain solves, insuring that there is multiphysics coupling during all aspects of the algorithm. The fluid-structure system is discretized on unstructured nonnested meshes, with an overlapping additive domain decomposition on both coarse and fine levels and multiplicative Schwarz preconditioning between levels. We investigate the effect of different coarse discretization sizes, solver stopping criteria, and overlap size, and we demonstrate that the method is robust to physical parameters including the structure's Young's modulus and the timestep size. Finally, we show effective preconditioning of the complicated coupled system, with nearly perfect weak scaling to a thousand processors and millions of unknowns.Key words. fluid-structure interaction, blood flow, multilevel methods, arbitrary LagrangianEulerian, restricted additive Schwarz, domain decomposition, parallel computing, preconditioning AMS subject classifications. 65M55, 65M60, 65Y05, 76Z05 DOI. 10.1137/0907794251. Introduction. Fluid-structure interaction problems are difficult enough that simulations of realistic phenomena often require parallel processing. In this paper we consider scalable and efficient two-level Newton-Krylov-Schwarz algorithms for monolithic coupling in fluid-structure interaction. The target application is blood flow in arteries, which is a computationally difficult and practically important application area [15,36]. In particular, the similar densities of blood and artery wall make the coupling between fluid and structure strong in both directions, so that partitioned or iterative procedures have difficulties due to the added-mass effect [1,8]. Instead of a partitioned procedure, we adopt a monolithic computational approach, coupling fluid to structure in one large system that is solved all at once. This tight coupling allows for robustness to parameters and makes our method immune to the addedmass effect. The resulting system is difficult to solve, but we show here that it can be solved efficiently with effective preconditioning strategies. For more on monolithic coupling, see [5,16,21]. Though we focus on the blood-flow problem, our algorithm could be used for more general fluid-structure interaction problems, including ones with deformable structures inside the fluid domain [25].Besides monolithic coupling in all aspects of the numerical algorithm, the other emphasis of our approach is parallel scalability. Fluid-structure interaction problems in general, and the blood-flow problem in particular, are very computationally demanding and require parallel computing in order to achieve useful resolution and accuracy. In order to use large supercomputers for large problems, we need innovative

show abstract

Section: A Fully Coupled Model Our Incompressible Linear Visco-elastmentioning

confidence: 93%

Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction

Barker¹,

Cai²

2010

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…One of the first applications of the Equipotential technique (Winslow (1963) andWinslow (1981)) to distribute mesh velocity from moving boundaries has been done by Benson (1989).…”

Section: Laplacian Reviewmentioning

confidence: 99%

Robust moving-mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems

Landry

Soulaïmani

Luke

et al. 2016

54th AIAA Aerospace Sciences Meeting

View full text Add to dashboard Cite

ACKNOWLEDGEMENTSI would like to express my gratitude:• To my thesis supervisor Azzeddine Soulaïmani Ph.D., Eng. Professor Soulaïmani has given me the chance to explore a complex subject with freedom and trust. I have also gained a lot from his mentoring, reputation, experience and our long discussions for which I am truly grateful;• To Amine Ben Haj Ali Ph.D. for his help on defining the test cases and his experiences in meshing generation;• To Professor Edward Luke Ph.D. who shared with us his mesh-mover algorithm which was crucial to generate great results and study deeper the subject of moving boundaries problems;• To Aziz Madrane Ph.D. for his recommendation on the use of the ADT search algorithm.Also, a special thanks to the École de technologie supérieure for entrusting me the excellence scholarship which allowed me to dedicate my energy completely to this research with the support of this growing institution.I dedicated this work to my dear fiancée Alicia who allowed me to push myself every day and to produce proudly this thesis thanks to her love and her motivation; à ma mère Colette, mon père Georges, mon frère Nicholas et ma soeur Maude pour leur soutien inconditionnel; to all my friends who have help me grow; and to Botas and Rizpita whom entertain me during my redaction. MÉTHODES ROBUSTES DE MOUVEMENT DE MAILLAGES HYBRIDES: APPLICATION AUX PROBLÈMES DE FRONTIÈRES MOBILESJonathan LANDRY RÉSUMÉ L'objectif principal de ce mémoire est de développer un Algorithme de Mouvement de Maillage (AMM) suffisament robuste qui sera capable d'adapter les maillages de la majorité des problèmes de frontières mobiles. Ainsi, une nouvelle méthodologie est implémentée à partir de la meilleure combinaison provenant d'algorithmes connus dans le but de mieux préserver la qualité des maillages initiaux.Dans la majorité des simulations, les AMMs standards sont capables de déplacer le maillage en conservant une bonne qualité de maillage, toutefois quand le mouvement est complexe et/ou qu'il y a une interaction multi-corps ils génèrent des maillages invalides. Alors, la nouvelle approche est constituée de trois algorithmes: la fonction pondérée de la distance inverse (PDI) pour produire le champ de déplacements, les algorithmes de lissages de la Méthode de Transformation Géométrique d'Élément (MéTGÉ) pour améliorer la qualité du maillage résultant et un nouvel algorithme basé sur la MéTGÉ qui est capable de réparer les maillages invalides. Il a été prouvé qu'avec cette méthodologie des problèmes de frontières mobiles très difficiles peuvent être résolus.L'approche proposée a été démontrée efficace pour adapter les maillages de différentes situations aéroélastiques réalistes: une aile symétrique a subi une grande flexion et une grande torsion induites au bout de l'aile; et les dispositifs hypersustentateurs de deux ailes (une rectangulaire et une avec une flèche) ont été déplacés vers différentes positions de vol.Finalement, il a été prouvé qu'avec la méthode proposée, la majorité des maillages pour les problèmes d'IFS peuvent ê...

show abstract

“…In the CAVEAT code [13], the whole computation region is remeshed and the material interfaces are restored by removing the velocity component normal to the interfaces, whereas in our ALE method, material interfaces are determined in Lagrangian motion at first, and the rezoning is performed in each material region, such that nodes on interfaces can be redistributed to improve the mesh quality. An algorithm for adaptive mesh generation based on the following elliptic equations is adopted to implement the rezoning [22]:…”

Section: Rezone and Remap Phase 2221 Rezonementioning

confidence: 99%

An arbitrary Lagrangian–Eulerian method based on the adaptive Riemann solvers for general equations of state

Tian

Shen

Jiang

et al. 2008

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYApproximate or exact Riemann solvers play a key role in Godunov-type methods. In this paper, three approximate Riemann solvers, the MFCAV, DKWZ and weak wave approximation method schemes, are investigated through numerical experiments, and their numerical features, such as the resolution for shock and contact waves, are analyzed and compared. Based on the analysis, two new adaptive Riemann solvers for general equations of state are proposed, which can resolve both shock and contact waves well. As a result, an ALE method based on the adaptive Riemann solvers is formulated. A number of numerical experiments show good performance of the adaptive solvers in resolving both shock waves and contact discontinuities.

show abstract

Adaptive-mesh zoning by the equipotential method

Cited by 82 publications

References 0 publications

Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction

Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction

Robust moving-mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems

An arbitrary Lagrangian–Eulerian method based on the adaptive Riemann solvers for general equations of state

Contact Info

Product

Resources

About