The Discontinuous Galerkin Method and its Implementation in the RAMEG3D Software Package

Currently, the Discontinuous Galerkin Method (DGM) is widely used to solve complex multi-scale problems of mathematical physics that have important applied significance. When implementing it, question choosing a discrete approximation flows for viscous terms Navier-Stokes equation important. It necessary focus on construction limiting functions, selection best approximations diffusion flows, and use implicit iterative methods solving obtained differential-difference equations successful application DGM three-dimensional unstructured grids. First-order numerical schemes second-order with Godunov, HLLC, Rusanov-Lax-Friedrichs hybrid are investigated. For high-order precision methods, it time schemes. The Runge-Kutta scheme third order in work. written as system first-order equations, when by discontinuous method.