Bubble Rise Velocity in Multiphase LBM

[asafi]

Hi everyone,rnrnI am using the Shan-Chen single component, multiphase model to simulate the rise of a single bubble under density ratio of 10 and Eö number of 10.rnThe boundary conditions are the same as the so-called TP2D finite element benchmark (Hysing and Turek 2007)…. so a 2d box of size 1×2, with the no-slip boundary condition on top and bottom and slip b.c. on the sides. The initial radius of the bubble is 0.25.rnrnWell… the position and the shape of the bubble matches those in TP2D benchmark. HOWEVER, the average fluid velocity inside the bubble is around (not exactly) 3.0 times larger than the actual rise velocity of the bubble. I calculate the rise velocity like this rnrnV_rise = d(y_cent) / dtrnrnusing a forward Euler approximation, where y_cent is the centroid of the bubble. The average bubble velocity is obtained like rnrnV_bubble = Sum(u)/Nrnrnwhere N is the number of lattice points inside bubble, u is the fluid velocity and the Sum is taken over the fluid nodes inside the bubble.rnrnSo, surprisingly I get rnrnV_bubble = 3.0 V_risernrnwhile logically and physically they should be identical!!! It looks like the fluid inside is moving faster than the bubble itself!!!rnrnDoes any one have any idea what might have caused such a paradox!? I would be really grateful :)rnrnAmin

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