We construct the molecular model and the tensor model for the dynamics of the nematic phases of bent-core molecules and star molecules in incompressible fluid. We start from the molecular interaction and the molecule fluid friction, and write down a general formulation based on the molecular shape and the free energy. Then we incorporate an Onsager-theory-based static tensor model to obtain the dynamic molecular model fully determined by the molecular architecture. The tensor model is obtained by adopting the quasi-equilibrium approximation that maintains energy dissipation. For bent-core molecules and star molecules that have the same molecular symmetry, the form of the model is identical. The molecular architecture is differentiated by the coefficients that are derived as functions of molecular parameters. Numerical simulation is carried out for the shear flow problem using both the molecular and the tensor models, focusing on the effect of altering molecular architecture. When the equilibrium phase is biaxial, novel flow modes are found, and the flow mode sequences show delicate dependence on the molecular architecture. The tensor model proves to exhibit all the flow modes found in the molecular model.