High order accurate discontinuous Galerkin (DG) methods can offer tangible advantages in engineering and science applications. The talk will begin with a brief overview of DG methods, and how to apply them to a simple linear advection model. We then jump to some large-scale application problems. First, coastal engineering applications using the shallow water equations will be presented for large-scale validation problems in hurricane storm surge and coastal flooding. Next we will discuss how to extend the shallow water equation model to support geophysical flows and erosion, as accomplished by coupling to the Exner equations. Finally we discuss some applications in high energy plasma dynamics, where turbulent saturation in nonlinear plasma can be used to model and predict the behavior of scrape-off layer dynamics in the presence of resonant magnetic pulses near plasma material interfaces in tokamaks.