Applications of discontinuous Galerkin method in numerical simulations of compressible flows:A review

In this paper, we give a review on the international and domestic applications of the promising high-order method(HOM), the discontinuous Galerkin method (DGM), in the numerical simulation of compressible flows over the last three decades. A brief introduction of the basic concepts and attributes of the DGM is given first. Then a historical survey on the DGM's applications in solving hyperbolic and elliptical equations is presented, mainly concentrating on its development and research status in the field of computational fluid dynamics (CFD). Existing challenges and possible trends in the aspects of corresponding mesh technologies, shockwave capturing methods, turbulence simulation, and computational resource requirement are concluded and analyzed as well. Several examples of its applications in the simulation of compressible flows are provided at last.