An efficient implicit procedure for the Discontinuous Galerkin (DG) method is developed utilizing a pointwise relaxation algorithm. In the pointwise relaxation, those contributions from the degrees of freedom in own computational cell are accounted for in the implicit matrix inversion. The resulting scheme is shown to be stable with very large CFL numbers for both the Euler and the Navier-Stokes equations for typical test problems. In order to achieve a faster convergence, efforts are also made to reduce computing time of the present method by utilizing a p-multigrid scheme and also by solving a simplified matrix instead of a fully loaded dense matrix in the implicit matrix inversion. A superior performance of the present implicit DG method on the parallel computer using up to 128 PEs is shown in terms of readily achievable scalability and high parallel efficiency. The RANS simulation of turbulent flowfield over AGARD-B model is carried out to show the convergence property and numerical stability of the present implicit DG method for engineering applications.
Bow-shock instability has been experimentally observed in a low-γ flow. To clarify its mechanism, a parametric study was conducted with three-dimensional numerical simulations for specific heat ratio γ and Mach number M. A critical boundary of the instability was found in the γ-M parametric space. The bow shock tends to be unstable with low γ and high M, and the experimental demonstration was designed based on this result. The experiments were conducted with the ballistic range of the single-stage powder gun mode using HFC-134a of γ = 1.12 at Mach 9.6. Because the deformation of the shock front was observed in a shadowgraph image, the numerical prediction was validated to some extent. The theoretical estimation of vortex formation in a curved shock wave indicates that the generated vorticity is proportional to the density ratio across the shock front and that the critical density ratio can be predicted as ∼10. A strong slipstream from the surface edge generates noticeable acoustic waves because it can be deviated by the upstream flow. The acoustic waves emitted by synchronizing the vortex formation can propagate upstream and may trigger bow-shock instability. This effect should be emphasized in terms of unstable shock formation around an edged flat body.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.