We simulate crystal growth from solution using the Monte Carlo method in the semigrand-isobaric-isothermal ensemble. All crystals are grown in the face-centered-cubic (100) direction, while varying the solubility and temperature. This enables us to change the growth mode from linear to nonlinear. In order to simulate at time scales necessary for growth from solution, we devised and used smart Monte Carlo moves. These moves enhance the solute-solvent interdiffusion processes, similar to convection in experimental situations, while leaving the kinetics in the adsorption layer between the crystal and the solution unaffected. These kinetics then become the rate determining step. The structure and dynamics of the interfacial region is investigated quantitatively, leading to the conclusion that especially during rough, three-dimensional growth, trapping of solvent particles in newly grown crystal layers is the rate determining process.