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Fictitious Domain Methods and Computation of Homogenized Properties of Composites with a Periodic Structure of Essentially Different Components
Published in Guri I. Marchuk, Numerical Methods and Applications, 2017
Conditions (2.2) correspond to porous media, with the subdomain D⊥ constituting a set of cavities. Such media can be treated as perforated composite material. We prove in Section 2.3 that problem (2.1) with Equation (2.2) is the problem of the Fictitious Domain Method applied to the Neumann boundary value problem in V.
Translation simulation of a cylinder in a horizontal pipe
Published in Engineering Applications of Computational Fluid Mechanics, 2019
Benchun Yao, Qingxin Ding, Kang Zhang, Defu Yang, Xiaoxiao Zhu
In the Eulerian–Lagrange approach, the flow field is obtained by calculating the Navier–Stokes (N-S) equation in the Euler frame, whereas every dispersed object is tracked with the Lagrangian approach by solving Newton's dynamic equation (Göz et al., 2006). To capture the total dynamic force applied on the object, the instantaneous surface of the object should be determined accordingly. There are also two specific methods to treat the moving surface. The first is the non-geometry-conforming grid method wherein the solid–fluid domain is computed with a fixed and uniform mesh to avoid frequent re-meshing, which is usually called the ‘fictitious domain method’ (Uhlmann, 2005; Uhlmann & Dušek, 2014). The second uses a dynamic fluid domain, subject to the no-slip condition at interfaces with solid objects (Uhlmann, 2005). In FLUENT® (Andy's, Inc. Canonsburg, PA, USA), it is called the dynamic mesh technique and it is widely used in the simulation of particle motion in pipes. It can be used to simulate the falling of a cylinder in a vertical tube (Schaschke, 2010), or to investigate the piston effect of a train in subway tunnel (Kim & Kim, 2007, 2009; López González, Galdo Vega, Fernández Oro, & Blanco Marigorta, 2014; Xue, You, Chao, & Ye, 2014).
Numerical study of the wall effect on particle sedimentation
Published in International Journal of Computational Fluid Dynamics, 2018
Liang-Hsia Tsai, Chien-Cheng Chang, Tsorng-Whay Pan, Roland Glowinski
In order to avoid frequent re-meshing and the difficulties associated with mesh generation on a time varying domain when the particles are very close to each other (also a very common situation in 3D), we have used a fictitious domain approach extending the governing equations to the entire domain as developed in Glowinski et al. (2001). The basic idea of the fictitious domain method is to suppose that the fluid fills the entire space inside as well as outside the particle boundary. The fluid-flow problem is then posed on a larger domain (the ‘fictitious domain’). The fluid inside the particle boundary must exhibit a rigid-body motion. This constraint is enforced using a distributed Lagrange multiplier, which represents the additional body force needed to maintain the rigid-body motion inside the particle boundary, much like the pressure in incompressible fluid flow, whose gradient is the force required to maintain the incompressibility condition. Assuming (without loss of generality) that the fluid–particle mixture contains only one particle , the fictitious domain based variational formulation of the governing equations (1)–(9) reads as follows: