Keywords: finite element method, fictitious domain method, Lagrange multiplier, Navier-Stokes equations, delta function, fluid force.

The purpose of this paper is to analyze the fluid and moving boundary problem using the fictitious domain method with Lagrange multipliers. The incompressible Navier-Stokes equation is used in this paper. To solve this equation, a fictitious domain method with Lagrange multipliers is applied. For the analysis of the finite element method, the mixed interpolation based on the bubble function is presented. In the fictitious domain method, remeshing is not necessary. Additionally, the calculation time is decreased, and the amount of memory required is reduced. It is necessary to approximate by using an interpolation function for the Lagrange multiplier. However, it is difficult to integrate the formula. The Delta function of Dirac is used here. Two kinds of meshes are used for the fictitious domain method. One of the meshes is used as the computational domain, the other is used as a bounded domain. In this research, the object moved by the fluid force (drag force) is analyzed in three dimensions. In the fictitious domain method, it is easy to obtain the fluid force, because 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 the fictitious domain method based on distributed Lagrange multipliers are investigated.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £125 +P&P)