We develop a properly parameterized, three-dimensional continuum-scale kinetic model for monitoring the surface morphological evolution of coherently strained heteroepitaxial thin films that captures the morphological response of epitaxially grown Ge thin films on pit-patterned Si{100} substrates. The model accounts for curvature-driven atomic diffusion on the film surface, biaxial lattice misfit strain in the film, and the wetting potential between the film and the substrate. Selfconsistent dynamical simulations based on our model show formation of complex nanostructures on the epitaxial film surface, including nanorings at the rims of pits, a single quantum dot at the center of a pit, as well as multiple quantum dots inside pits with rectangular openings, consistent with experimentally observed nanostructures. Our simulation results reproduce the variation in the formed nanostructural features observed experimentally by properly varying the key experimental parameters, namely, the pit size and the pit geometry. Our study sets the stage for designing systematic experimental protocols toward precise control of complex nanoring and quantum dot patterns forming on surfaces of epitaxially grown coherently strained semiconductor thin films.