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The Young–Laplace equation describes the stress balance between the interfacial tension and the gravitational body force. Its modified form can be applied to model the dynamics of the interface of the two-phase flow. It is analytically difficult to solve the Young–Laplace equation due to its strong nonlinearity, in the form of the surface curvature and the implicit body force on the interface. This work aims to numerically solve the Young–Laplace equation with a finite-volume method (FVM) and an overlapped grid. The overlapped grid allocates the variable and its derivative together at every grid point, and is compared with the traditional staggered grid. The proposed overlapped grid can achieve fourth-order numerical accuracy, which is higher than the second-order accuracy of the staggered grid. Also, the overlapped grid, with full states defined at every grid point, offers convenience to the implementation of the boundary condition as well as the coupling of multi-physics.

Solution of young–Laplace equation with finite-volume method and overlapped grid