By using the Onsager variational principle as an approximation tool, we develop a new diffusion generated motion method for wetting problems. The method uses a signed distance function to represent the interface between the liquid and vapor surface. In each iteration, a linear diffusion equation with a linear boundary condition is solved for one time step in addition to a simple re-distance step and a volume correction step. The method has a first-order convergence rate with respect to the time step size even in the vicinity three-phase contact points. Its energy stability property is analysed by careful studies for some geometric flows on substrates. Numerical examples show that the method can be used to simulate complicated wetting problems on inhomogeneous surfaces.

通过使用Onsager变分原理作为逼近工具，我们开发了一种新的扩散生成的润湿方法运动方法。该方法使用带符号的距离函数表示液体和蒸汽表面之间的界面。在每次迭代中，除了简单的重新距离步骤和体积校正步骤外，还需要求解具有线性边界条件的线性扩散方程一个时间步长。该方法即使在附近的三相接触点中也具有相对于时间步长的一阶收敛率。通过仔细研究基底上的某些几何流动，分析了其能量稳定性。数值算例表明，该方法可用于模拟非均匀表面上复杂的润湿问题。