Parallel nodal interior-penalty discontinuous Galerkin methods for the subsonic compressible Navier–Stokes equations: Applications to vortical flows and VIV problems

We present a novel Interior-Penalty (IP) Discontinuous Galerkin (DG) solver for the compressible Navier–Stokes system, designed for applications of technological and industrial interest in the subsonic region. The new IP term: σ , which is derived face-wise based on inverse estimates, is sensitive to the local face-adjacent elements’ size, the polynomial order and the magnitude of the local non-linear diffusion tensor. Its adverse effect on the control of the explicit time-step through a CFL condition is also revealed. Ultimately, the new penalty’s free parameter admits values that are able to guarantee the positivity of the diffusion operator without sacrificing much of the computational robustness of the system’s purely hyperbolic part. The compact stencil offered by the IP flux is further shortened using nodal bases. Also, triangular elements are used which offer a memory advantage regarding storage of local DG matrices. The resulting algorithm was found to be scalable up to 17,920 MPI cores, indicating its ability to handle large numbers of degrees of freedom efficiently. The resulting framework successfully implements polynomial orders of p ≥ 4 and is firstly tested in terms of its convergence properties. Then, numerical solutions are validated with experimental and numerical data for the case of a circular cylinder at low Reynolds numbers, and lastly, the methodology is employed to simulate the vortex-induced vibrations (VIV) of an elastically-mounted cylinder, a known configuration characterised by significant computational challenges. The above results showcase that the IPDG framework can be employed as an accurate and efficient, arbitrary-order numerical methodology for high-fidelity fluid–structure-interaction (FSI) problems.