[논문]Finite element analysis of elastic solid/Stokes flow interaction problem

Myung, Jin-Suk; Hwang, Wook-Ryol; Won, Ho-Youn; Ahn, Kyung-Hyun; Lee, Seung-Jong

Finite element analysis of elastic solid/Stokes flow interaction problem 원문보기

Korea-Australia rheology journal, v.19 no.4, 2007년, pp.233 - 242

Myung, Jin-Suk (School of Chemical and Biological Engineering, Seoul National University) , Hwang, Wook-Ryol (School of Mechanical and Aerospace Engineering, Research Center for Aircraft Parts Technology (ReCAPT), Gyeongsang National University) , Won, Ho-Youn (Hanwha Chemical, Research and Development Center) , Ahn, Kyung-Hyun (School of Chemical and Biological Engineering, Seoul National University) , Lee, Seung-Jong (School of Chemical and Biological Engineering, Seoul National University)

Abstract ▼ AI-Helper

We performed a numerical investigation to find out the optimal choice of the spatial discretization in the distributed-Lagrangian-multiplier/fictitious-domain (DLM/FD) method for the solid/fluid interaction problem. The elastic solid bar attached on the bottom in a pressure-driven channel flow of a Newtonian fluid was selected as a model problem. Our formulation is based on the scheme of Yu (2005) for the interaction between flexible bodies and fluid. A fixed regular rectangular discretization was applied for the description of solid and fluid domain by using the fictitious domain concept. The hydrodynamic interaction between solid and fluid was treated implicitly by the distributed Lagrangian multiplier method. Considering a simplified problem of the Stokes flow and the linearized elasticity, two numerical factors were investigated to clarify their effects and to find the optimum condition: the distribution of Lagrangian multipliers and the solid/fluid interfacial condition. The robustness of this method was verified through the mesh convergence and a pseudo-time step test. We found that the fluid stress in a fictitious solid domain can be neglected and that the Lagrangian multipliers are better to be applied on the entire solid domain. These results will be used to extend our study to systems of elastic particle in the Stokes flow, and of particles in the viscoelastic fluid.

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제안 방법

solid/Stokes flow interaction problem. The purpose of this numerical work is to find 이it the proper condition in using the DLM/FD scheme to the solid/fluid interaction problem. The robustness of this simulation algorithm has been verified through the mesh convergence and pseudo time step dependence test.
Also, to assess the necessity of considering fluid stress in the solid domain, we denote a problem with sub-matrices I and P by SV and a problem without I and P by V The four sets, two different conditions for each factor, have been listed in Table 1. To understand the effect of each factor and to find the opti mum condition, we performed numerical experiments for the four sets and checked the mesh convergence and the pseudo-time step dependence to evaluate the robustness of the present formulation. The results are presented from all four sets together for the proper comparison.

이론/모형

Using the fictitious domain method, one can avoid remeshing and solve the problem with a simple regular mesh, which is especially beneficial in 3D simulation. In this study, the fictitious domain method will be used with which constraints on the solid boundary (or over the solid domain) are represented by the distributed Lagrangian multipliers (Glow inski et aL.,1999). The overview of the distributed- Lagrangian-multiplier/fictitious-domain(DLM/FD) method is well documented in Glowinski et al.
In this study, we apply the distributed-Lagrangian-mul-tiplier/fictitious-domain (DLMZFD) method to a simple elastic solid/Stokes flow interaction problem. We investi gate the effect of the distribution of the Lagrangian multipliers and the effect of interfacial conditions between the fluid and solid meshes.
The purpose of this numerical work is to find 이it the proper condition in using the DLM/FD scheme to the solid/fluid interaction problem. The robustness of this simulation algorithm has been verified through the mesh convergence and pseudo time step dependence test. All four sets showed good mesh convergence, and there was no pseudo-time step depen dence.
In the solid domain a regular rectangular discretization is also used but with the bi-linear interpolation of the displace ment and the constant pressure element (Qi~PQ element). To impose no-slip constraint on the solid boundary, we applied the distributed Lagrangian multiplier method. For the computational convenience, multipliers are imposed on every nodal point on the solid boundary (or on the solid domain).

참고문헌 (14)

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