Abstract
The purpose of this paper is to analyze the fluid and moving boundary problem by fictitious domain method with Lagrange multiplier. The incompressible Navier-Stokes equation is used in this paper. To solve this equation, fictitious domain method with Lagrange multiplier is applied. For the analysis of the finite element method, the mixed interpolation based on the bubble function is presented. In fictitious domain method, this method is not necessary to remeshing. Additionally, the calculation time is decreased, and the amount of memory is reduced. It is necessary to approximate by using interpolation function for the Lagrange multiplier. However, it is dicult to integrate the formula. The Delta function of Dirac is used here. Two kinds of meshes are used for fictitious domain method. One of meshes is used as computational domain, the other is used as a bounded domain. In this research, it is analyzed to move the object by the fluid force (drag force) in 3-dimension. In fictitious domain method, it is easy to obtain the fluid force. Because it is defined the Lagrange multiplier is equal to the traction in each node on a bounded domain. The pressure and flow velocity when the object moves are verified. And advantages of fictitious domain method based on distributed Lagrange multiplier are investigated.
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