  We present discontinuous Galerkin (DG) methods for solving a first-order
semi-linear hyperbolic system, which was originally proposed as a continuum
model for a one-dimensional dimer lattice of topological resonators. We examine
the energy-conserving or energy-dissipating property in relation to the choices
of simple, mesh-independent numerical fluxes. We demonstrate that, with certain
numerical flux choices, our DG method achieves optimal convergence in the $L^2$
norm. We provide numerical experiments that validate and illustrate the
effectiveness of our proposed numerical methods.
