title: Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules.
abstract: 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.
authors.affiliation: Department of Mathematics, University of California, San Diego, CA 92093.
authors.forename: Hui
authors.initials: H
authors.lastname: Sun
authors.affiliation: School of Mathematical Sciences and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, Jiangsu 215006, China.
authors.forename: Shenggao
authors.initials: S
authors.lastname: Zhou
authors.affiliation: Department of Physics, University of California, San Diego, CA 92093.
authors.forename: David K
authors.initials: DK
authors.lastname: Moore
authors.affiliation: Department of Mathematics, University of California, San Diego, CA 92093.
authors.forename: Li-Tien
authors.initials: LT
authors.lastname: Cheng
authors.affiliation: Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, CA 92093.
authors.forename: Bo
authors.initials: B
authors.lastname: Li
keywords: Nonpolar molecules; change of volume; ghost fluid method; interface motion; level-set method; solute-solvent interface; the Stokes equation; traction boundary conditions