We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

中文翻译：

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非极性分子的斯托克斯溶剂流和溶质-溶剂界面动力学的数值处理。

我们设计和实现了用于非极性分子在水性溶剂中不可压缩的斯托克斯溶剂流量和溶质-溶剂界面运动的数值方法。粘性力，表面张力和范德华型分散力之间的平衡导致了溶质-溶剂界面上的牵引边界条件。为了允许溶质体积的变化，我们通过一致性条件在计算域的边界上设计了特殊的数值边界条件。我们使用有限差分重影流体方案来离散具有此类边界条件的斯托克斯方程。经过测试，该方法具有二阶精度。我们将此重影流体方法与水平设置方法结合起来，以模拟由溶剂流体速度控制的溶质-溶剂界面的运动。