This paper discusses the numerical solution of the incompressible viscous flow by the fictitious domain method with distributed Lagrange multiplier. For the analysis of the finite element method, the mixed interpolation based on the bubble function is presented. The way to use the fictitious domain method applied to the Navier-Stokes equation is explained. The incompressible viscous flow with two falling solid particles is presented. Advantage of the fictitious domain method based on distributed Lagrange multiplier is investigated.
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GlowinskiR.PanT. W.HeslaT. I.JosephD. D.PériauxJ., A Fictitious Domain Approach to the Direct Numerical Simulation of Incompressible Viscous Flow past Moving Rigid Bodies: Application to Particulate Flow, Journal of Computational Physics, 169, pp. 363–426, 2001.
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