We propose a hybrid lattice-Boltzmann finite-difference method to simulate axisymmetric multiphase flows. The hydrodynamics is simulated by the lattice-Boltzmann equations with the multiple-relaxation-time (MRT) collision model and suitable forcing terms that account for the interfacial tension and axisymmetric effects. The interface dynamics is captured by the finitedifference solution of the convective Cahn–Hilliard equation. This method is applied to simulate a quiescent drop, an oscillating drop, a drop spreading on a dry surface and a drop accelerated by a constant body force. It is validated through comparisons of the computed results for these problems with analytical solutions or numerical solutions by other different methods. It is shown that the MRT-based method is able to handle more challenging cases than that with the single-relaxation-time collision model for axisymmetric multiphase flows due to its improved stability. PACS numbers: 47.11.−j, 47.55.D−
4 Figures and Tables
Figure 2. Comparison of the maximum velocity magnitude √ u2 + v2|max evolutions by the 2nd scheme and the iso scheme with Re = 1 × 103, Ca = 1, Cn = 0.2, Pe = 4 × 103, Nx = 20 and Nt = 80.
Figure 3. Comparison of the maximum velocity magnitude √ u2 + v2|max evolutions by the SRTand MRT-based hybrid LB-FD method at Re = 1×103, 1×104, 1×105, with Ca = 1, Cn = 0.2, Pe = 2 × 103, Nx = 20 and Nt = 80.
Figure 4. Comparison of the evolutions of the drop radius on the x-axis Rx at four different Reynolds numbers, Re = 100, 200, 400 and 1000, with Ca = 1, Cn = 0.1, Pe = 4× 103, Nx = 32 and Nt = 256.
Figure 6. Snapshots of the interface and velocity field at t = 0, 10, 20, 30, 40, 50 by MRT-LB-FD with Re = 20, Ca = 1, Cn = 0.1, Pe = 5 × 103, Nx = 32 and Nt = 256.
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