Modelling one-dimensional unsteady flows in ducts: Symmetric finite difference schemes versus Galerkin discontinuous finite element methods (Q1372528)

For calculation of unsteady one-dimensional flows in ducts, several numerical schemes are considered. Namely, the authors examine in detail two-step Lax-Wendroff and MacCormack predictor-corrector schemes coupled with FCT technique via smoothing and via damping, TVD algorithm by Davis, artificial compressibility method by Harten, and discontinuous Galerkin FEM. In FEM, an exact Riemann solver is used for approximation of flux function at cell interfaces, and ``viscous like'' term similar to the one presented in streamline diffusion FEM is added to ensure necessary amount of dissipation. For evaluation of integrals presented in FEM the authors use Gauss quadrature formulae, whereas for time discretization they use Runge-Kutta methods of the accuracy corresponding to space discretization rate. Two test problems are considered, and detailed comparison between these methods is given. In numerical calculations different CFL numbers are used for different numerical schemes, e.g. for Lax-Wendroff method the CFL number is set equal to 1, but for the third order FEM it is set equal to 0.2. Third order FEM is most accurate and time consuming.