An adaptive high order Reynolds-averaged Navier-Stokes solver with transition prediction

Abstract

The use of simulation techniques in applied aerodynamics has increased dramatically in the last three decades fostered by the growth in computational power. However, the state of the art discretization in industrial solvers remains nominally second order accurate, which makes them unfeasible to resolve multi-scale phenomena such as turbulence or acoustics, and limits their efficiency in terms of the error per degree of freedom. In recent years, the CFD community has put significant effort into the development of high order methods for fluid dynamics, with the goal of overcoming these barriers. This dissertation focuses on the application of high order hybridizable discontinuous Galerkin schemes to solve the equations that govern compressible turbulent flows. In particular, this thesis describes a novel methodology to adapt the boundary layer mesh to the solution "on the fly", based on a measure of the boundary layer thickness that drives the position of the nodes in the mesh, without changing its topology. The proposed algorithm produces accurate solutions with a reduced number of degrees of freedom, by leveraging the combination of mesh adaptivity with the high order of convergence of the discretization. In addition, the active tracking of the boundary layer reduces the nonlinear stiffness and improves the robustness of the numerical solution. A new shock capturing technique based on the addition of artificial viscosity is developed to handle shocks. The model is driven by a non-dimensional form of the divergence of the velocity, designed so that sub-cell shock resolution is achieved when a high order discretization is used, independently of the element size. The approach is extended to include the effect of transition to turbulence using an envelope eN method. This takes advantage of the structure of the mesh and requires the solution of a surface PDE for the transition criterion, which is discretized using a novel surface hybridizable discontinuous Galerkin scheme. The resulting method can simulate transition to turbulence in attached and separated flows, and can also accommodate long-scale unsteadiness in which the transition location evolves in time.