Using a connectivity matrix, we establish a continuum modeling approach with partial differential equations of conservation laws for simulating materials flow in supply chain networks. A number of existing and new constitutive relationships for modeling velocity are summarized or proposed. To effectively treat strong advection components within the modeling system, we apply discontinuous Galerkin (DG) methods for solving production flow in a supply chain network. In addition, a number of DG properties are analyzed for treating network flow. In particular, a nearly optimal error estimate is obtained using a new estimating technique that utilizes two physical meaningful assumptions on the connectivity matrix. Numerical examples are provided to simulate a single node, a serial supply chain and an entire network as well as to investigate the influence of influx variation and node shut-down to the profiles of work in progress (WIP) and outflux. It is shown that the proposed modeling approach is applicable to a large number of scenarios including re-entrant lines and the proposed DG algorithm is robust and accurate for predicting WIP and outflux behaviors.