GRACE-DG: A Discontinuous Galerkin method-based code for general non-linear coagulation-fragmentation equations

Dust plays a crucial role in protoplanetary disks (PPDs) evolution and planet formation, influencing disk dynamics through gas-dust coupling, regulating disk temperature by dominating continuum opacity, and altering disk ionization fraction by capturing free electrons. In this work, we develop a high-order discontinuous Galerkin (DG) method-based open-source code GRACE-DG to solve the collision-induced coagulation-fragmentation equations. In particular, we have derived a new conservative formulation for the non-linear fragmentation term, which enables the DG method to capture the mass transfer process. The new solver exhibits good convergence in coupled aggregation and breakage simulations, making it highly suitable for future integration into hydrodynamic codes.