For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity. ...For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phasedensity equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves,such as shear waves in fluids, are introduced by the artificial treatment. In this paper,a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.展开更多
In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mas...In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.展开更多
In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows ar...In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11702029,11771054,U1730118,91852207,and 11801036)the China Postdoctoral Science Foundation(No.2016M600967)
文摘For solid-fluid interaction, one of the phase-density equations in diffuse interface models is degenerated to a "0 = 0" equation when the volume fraction of a certain phase takes the value of zero or unity. This is because the conservative variables in phasedensity equations include volume fractions. The degeneracy can be avoided by adding an artificial quantity of another material into the pure phase. However, nonphysical waves,such as shear waves in fluids, are introduced by the artificial treatment. In this paper,a transport diffuse interface model, which is able to treat zero/unity volume fractions, is presented for solid-fluid interaction. In the proposed model, a new formulation for phase densities is derived, which is unrelated to volume fractions. Consequently, the new model is able to handle zero/unity volume fractions, and nonphysical waves caused by artificial volume fractions are prevented. One-dimensional and two-dimensional numerical tests demonstrate that more accurate results can be obtained by the proposed model.
文摘In this paper, we present two second-order numerical schemes to solve the fourth order parabolic equation derived from a diffuse interface model with Peng-Robinson Equation of state （EOS） for pure substance. The mass conservation, energy decay property, unique solvability and L~ convergence of these two schemes are proved. Numerical results demon- strate the good approximation of the fourth order equation and confirm reliability of these two schemes.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11425210,11621202 and 11672288)
文摘In this paper, we investigate flows with moving contact lines on curved solid walls on a dual-resolution grid using a diffuse-interface immersed-boundary（DIIB） method. The dual-resolution grid, on which the flows are solved on a coarse mesh while the interface is resolved on a fine mesh, was shown to significantly improve the computational efficiency when simulating multiphase flows. On the other hand, the DIIB method is able to resolve dynamic wetting on curved substrates on a Cartesian grid, but it usually requires a mesh of high resolution in the vicinity of a moving contact line to resolve the local flow. In the present study, we couple the DIIB method with the dual-resolution grid, to improve the interface resolution for flows with moving contact lines on curved solid walls at an affordable cost. The dynamic behavior of moving contact lines is validated by studying drop spreading, and the numerical results suggest that the effective slip length λ_n can be approximated by 1.9Cn, where Cn is a dimensionless measure of the thickness of the diffuse interface. We also apply the method to drop impact onto a convex substrate, and the results on the dual-resolution grid are in good agreement with those on a single-resolution grid. It shows that the axisymmetric simulations using the DIIB method on the dual-resolution grid saves nearly 60% of the computational time compared with that on a single-resolution grid.
