Hello Aritra,
Welcome to the MOOSE community! There are several examples of phase-field simulations of grain growth located in the MOOSE repository, in the directory
moose/modules/phase_field/examples/grain_growth/
(If you haven't done so already, start by installing MOOSE using the instructions located at https://mooseframework.org/getting_started/index.html.)
You can also look at the documentation for the grain growth model at:
https://mooseframework.inl.gov/old/wiki/PhysicsModules/PhaseField/GrainGrowthModel/
This gives the citation for the paper the model is based on and details on its implementation.