Assessment of a high-order discontinuous Galerkin method for internal flow problems. Part I: Benchmark results for quasi-1D, 2D waves propagation and axisymmetric turbulent flows. (1st August 2016) - Bartolo, C. De; Nigro, A.; Covello, V.; Bassi, F.
Highlights: A high-order DG scheme has been applied to internal flow problems. High-order is effective for waves propagation in quasi-1D, 2D ducts on coarse grids. Quasi-1D waves propagation doesn't require non-reflecting boundary conditions (NRBCs). Absorbing Sponge Layer BCs performed effectively for 2D waves propagation problems. DG scheme allows robust and high-order accurate RANS simulations of ICE flows. Abstract: In this work we apply a high-order discontinuous Galerkin (DG) finite element method to inviscid and turbulent internal flow problems. The equations here considered are the quasi-1D, 2D Euler equations and the RANS and k − ω equations in axisymmetric coordinates. The method here proposed is designed to ensure high-order accuracy in ducts and engine-like geometries using both explicit and implicit schemes for the temporal discretization of the governing equations. Absorbing Sponge Layer (ASL) boundary conditions are implemented to minimize the reflection of out-going waves at open boundaries. A shock-capturing technique is used to control the oscillations of high-order solutions around shocks. Accurate solutions of the hyperbolic equations are performed by means of the five-stage fourth-order accurate Strong Stability Preserving Runge-Kutta scheme, while the implicit Backward-Euler scheme is adopted for efficient steady state simulations of internal turbulent flows. Two types of test-problems have been considered, one focusing on the potential of DG method to solve ideal quasi-1D and 2D waves propagation and shock phenomena that may occur in ducts, and the other on its feasibility to provide high-order accurate solutions of multi-dimensional internal turbulent flows in geometries typical of internal combustion engine (ICE) applications. To clearly illustrate the performance of the high-order DG method, the results are compared with exact solutions, experimental data and second-order accurate solutions obtained with a finite volume commercial code.