▎ 摘　　要

We develop a paradigm for developing local energy dissipation rate preserving (LEDRP) approximations to general gradient flow models driven by source terms. In driven gradient flow models, the deduced energy density transport equation possesses an indefinite source. Local energy-dissipation-rate preserving algorithms are devised to respect the mathematical structure of both the driven gradient flow model and its deduced energy density transport equation. The LEDRP algorithms are also global energy-dissipation-rate preserving under proper boundary conditions such as periodic boundary conditions. However, the contrary may not be true. We then apply the paradigm to a phase field model for growth of a graphene sheet to produce a set of LEDRP algorithms. Numerical refinement tests are conducted to confirm the convergence property of the new algorithms and simulations of graphene growth are demonstrated to benchmark against existing results in the literature.