Fundamental biological molecular processes, such as protein folding, molecular recognition, and molecular assemblies, are mediated by surrounding aqueous solvent (water or salted water). Continuum description of solvent is an efficient approach to understanding such processes. In this work, we develop a solvent fluid model and computational methods for solvent dynamics and solute-solvent interface motion. The key components in our model include the Stokes equation for the incompressible solvent fluid which governs the motion of the solute-solvent interface, the ideal-gas law for solutes, and the balance on the interface of viscous force, surface tension, van der Waals type dispersive force, and electrostatic force. We use the ghost fluid method to discretize the flow equations that are reformulated into a set of Poisson equations, and design special numerical boundary conditions to solve such equations to allow the change of solute volume. We move the interface with the level-set method. To stabilize our schemes, we use the Schur complement and least-squres techniques. Numerical tests in both two and three-dimensional spaces will be shown to demonstrate the convergence of our method, and to demonstrate that this new approach can capture dry and wet hydration states as observed in experiment and molecular dynamics simulations.