Numerical simulation of rupture dynamics provides critical insights for understanding earthquake physics, while the complex geometry of natural faults makes numerical method development challenging. The discontinuous Galerkin (DG) method is suitable for handling complex fault geometries. In the DG method, the fault boundary conditions can be conveniently imposed through the upwind flux by solving a Riemann problem based on a velocity-strain elastodynamic equation. However, the universal adoption of upwind flux can cause spatial oscillations in cases where elements on adjacent sides of the fault surface are not nearly symmetric. Here we propose a nodal DG method with an upwind/central mixed-flux scheme to solve the spatial oscillation problem, and thus to reduce the dependence on mesh quality. We verify the new method by comparing our results with those from other methods on a series of published benchmark problems with complex fault geometries, heterogeneous materials, off-fault plasticity, roughness, thermal pressurization, and various versions of fault friction laws. Finally, we demonstrate that our method can be applied to simulate the dynamic rupture process of the 2008 Mw 7.9 Wenchuan earthquake along/across multiple fault segments. Our method can achieve high scalability in parallel computing under different orders of accuracy, showing high potential for adaptation to earthquake rupture simulation on natural tectonic faults.