Departmental Bulletin Paper 人の歩行による室内塵埃の飛散の3 次元解析のための数値計算法

中山 司  ,  本多 宏輝  ,  辻 紀子  ,  加藤 直朗

(第22号)  , pp.17 - 29 , 2017-03-31
A numerical method is proposed for the three-dimensional analysis of the scattering of dust in a room caused by human walk. The governing equations of çuid çow are the incompressible Navier-Stokes equations and the equation of continuity, and they are discretized by the ånite element method in space and by the ånite diãerence method in time. The discretized equations are assembled into a set of linear algebraic equations, which is solved by the conjugate residual method. The çuid region in a room is bounded partially by a moving boundary, that is the surface of a human body. To treat the moving boundary and the no-slip condition imposed on it numerically, the åctitious domain method is employed. The no-slip condition is considered as the subsidiary condition for the velocity åeld and is included into the weak form of the Navier-Stokes equations by using the Lagrangian method of undetermined multiplier. A dust is moved in a Lagrangian manner according to the çow velocity at the position of the dust. Numerical calculations by the proposed method have yielded the qualitative tendency of the dust motion caused by human walk. Encouraging results are obtained.

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