The domain composition method applied to Poisson's equation in two dimensions

Houzeaux

Computer Methods in Applied Mechanics and Engineering

et al. 2015

The implementations of an updated body-fitted and a non body-fitted method to deal with the interaction of a fluid and a rigid body are described. The physics of the fluid is modeled by the incompressible Navier-Stokes equations. A parallel fluid solver based on the VMS (Variational Multiscale) Finite Element method serves as the basis for the implementation. For the rigid body movement, the Newton-Euler equations are solved numerically. To account for the interaction, the force that the fluid exerts on the rigid body is determined, on the one hand. On the other hand, the velocity of the rigid body is imposed as a Dirichlet boundary condition on the fluid. A fixed Eulerian mesh discretizes the fluid domain, except for nodes in the vicinity of the rigid body boundary for the case of the updated body-fitted approach. The wet boundary of the rigid body is embedded in the fluid mesh and tracked by a moving surface mesh. It is a distinctive characteristic of the updated body-fitted strategy that, in order to impose velocities on the interface, some\ud of the nodes near the body surface are moved by using a local r-adaptivity algorithm to conform with this surface. By contrast, the non body-fitted approach uses kriging interpolation for velocity prescription over the fluid on the interface. Given that fluid nodes can become solid nodes and viceversa due to the rigid body movement, we have adopted the FMALE approach, a variation of the ALE method to keep the fluid mesh fixed. Algorithms to ensure high performance, like skd-trees to determine if a given spatial point is currently inside the solid, are also used. All these ingredients constitute two approaches that are both computationally efficient and accurate. Numerical experiments are presented to assess their performance comparatively.We would like to especially thank Oscar Peredo for his idea and support in introducing a more technical notation and terminology for the data-structures described in this work.Peer ReviewedPostprint (author's final draft

Section: Introductionmentioning

confidence: 99%

Parallel embedded boundary methods for fluid and rigid-body interaction

Houzeaux

Computer Methods in Applied Mechanics and Engineering

et al. 2015

“…Other local ÿelds, such as those for holes, can be introduced as shown by Strouboulis et al [2]. Overlapping meshes such as described by Charlesworth et al [26] could also be used. The method is similar to the ÿctitious element method of Glowinski et al [27]; the major di erence is the introduction of internal details and the description of the geometry by implicit functions.…”

Section: Discussionmentioning

confidence: 99%

Structured Extended Finite Element Methods of Solids Defined by Implicit Surfaces

Belytschko¹,

Mish²,

Moës³

et al. 2002

165

SUMMARYA paradigm is developed for generating structured ÿnite element models from solid models by means of implicit surface deÿnitions. The implicit surfaces are deÿned by radial basis functions. Internal features, such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended ÿnite element method. Methods for integrating the weak form for such models are proposed. These methods simplify the generation of ÿnite element models. Results presented for several examples show that the accuracy of this method is comparable to standard unstructured ÿnite element methods.

Journal of Computing and Information Science in Engineering

“…[14] combines the finite elements solutions on mapped domains with special functions. Some researchers suggested representing the domain as a Boolean (set) combination of premeshed primitives, in a manner similar to CSG representations used in early CAD systems [15,16].…”

Section: Domain Decomposition Methodsmentioning

confidence: 99%

Geometric Issues in Computer Aided Design/Computer Aided Engineering Integration

Shapiro

Tsukanov

Grishin

2011

The long-standing goal of computer aided design (CAD)/computer aided engineering (CAE) integration demands seamless interfaces between geometric design and engineering analysis/simulation tasks. The key challenge to this integration stems from the distinct and often incompatible roles geometric representations play, respectively, in design and analysis. This paper critically examines and compares known mesh-based and meshfree approaches to CAD/CAE integration, focusing on the basic tasks and components required for building fully integrated engineering applications. For each task, we identify the fundamental requirements and challenges and discuss how they may be met by known techniques and proposed solutions.