Journal of Scientific Computing

, Volume 67, Issue 2, pp 705–723 | Cite as

Numerical Treatment of Stokes Solvent Flow and Solute–Solvent Interfacial Dynamics for Nonpolar Molecules

  • Hui Sun
  • Shenggao Zhou
  • David K. Moore
  • Li-Tien Cheng
  • Bo Li


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.


Nonpolar molecules Solute–solvent interface The Stokes equation Ghost fluid method Level-set method Interface motion Change of volume Traction boundary conditions 



This work was supported by the US National Science Foundation (NSF) through grant DMS-1319731 and the US National Institutes of Health (NIH) through grant R01GM096188. Work in McCammon’s group is supported in part by NSF, NIH, HHMI, and NBCR. The authors thank Dr. Robert Krasny, Dr. Ray Luo, and Mr. Li Xiao for helpful discussions.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Hui Sun
    • 1
  • Shenggao Zhou
    • 2
  • David K. Moore
    • 3
  • Li-Tien Cheng
    • 1
  • Bo Li
    • 4
  1. 1.Department of MathematicsUniversity of CaliforniaSan DiegoUSA
  2. 2.School of Mathematical Sciences and Mathematical Center for Interdiscipline ResearchSoochow UniversitySuzhouChina
  3. 3.Department of PhysicsUniversity of CaliforniaSan DiegoUSA
  4. 4.Department of Mathematics and Quantitative Biology Graduate ProgramUniversity of CaliforniaSan DiegoUSA

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