As mentioned before, to solve the problem of convergence during calculation and test the sensitivity of results to the mesh density. A mesh of density 16 times compared with the former one is applied.

To achieve the above objectives, two group of parameters are used for the refine mesh:

A. A group of parameters same with one of those used for the coarse mesh, which is:

$$\rho_{water} /\rho_{oil}$$ (kg/m^{3}) |
$$\nu_{water} /\nu_{oil}$$ (Pa.s) | $$ \sigma_{oil/water} $$ (N/m) | $$ dt_{min}/dt_{max}$$ (s) | inlet/outlet lenght (m) | inlet velocity (m/s) | mesh size (m) | mesh size (cells) | inlet Re |

1000;800 | 2;20 | 0.487 | 0.45*0.35 | 0.2;0.025 | 2/5 | 0.45*0.35 | 360*280 | 20/50 |

B. The interface tension as initial values. Viscosity 10 times and 100 times to the initial values.

$$\rho_{water} /\rho_{oil}$$ (kg/m^{3}) |
$$\nu_{water} /\nu_{oil}$$ (Pa.s) | $$ \sigma_{oil/water} $$ (N/m) | $$ dt_{min}/dt_{max}$$ (s) | inlet/outlet lenght (m) | inlet velocity (m/s) | mesh size (m) | mesh size (cells) | inlet Re |

1000;800 | 0.01;0.1 | 0.025 | 0.1e-7;0.1e-4 | 0.02;0.025 | 1 | 0.45*0.35 | 360*280 | 2000 |

1000;800 | 0.1;1 | 0.025 | 0.1e-7;0.1e-4 | 0.02;0.025 | 1 | 0.45*0.35 | 360*280 | 200 |

When the viscosity is 10 times, the problem of convergence still exists. However, for the case where viscosity is 100 times, the calculation achieves convergence. For the group of parameters same with one of those adopted with the coarse mesh, the calculation converges; however it take almost 14 times to finish the simulation.

For case B, the movement of the fluids is similar with what we have obtained from the coarse mesh. Also, the interface between the two fluids is clearer.