Compressible Flows

The compressible flow group uses a solver which encapsulates two different sets of equation: the compressible Euler and Navier-Stokes equations. The problems are solved with a discontinuous projection of the field and using both a Discontinuous Galerkin and a flux reconstruction spatial discretisation. The topics of interest are:

  1. Inviscid transonic flow
  2. Supersonic flow
  3. High Reynolds number flow
  4. Goal-based error estimation
  5. p-adaption
  6. de-aliasing techniques
  7. flows over surface roughness

The figure below show the Q-criterion contour of a 3D Navier-Stokes simulation of a cylinder at Re = 3900 coloured by density.  It is possible to appreciate the fully turbulent wake generated behind the cylinder. Shocks occur at high Mach number flows. Numerical instabilities (Gibbs phenomena) occur around these flow discontinuities. These numerical fluctuations are damped by element wise adding artificial dissipation. Below, an example is shown of inviscid flow (M=2) past an Euler bump where a compression shock emerges above the bump and reflects on the upper side wall. The artificial dissipation is used using a non-smooth shock sensor. The adjoint solvers for the compressible Euler and Navier-Stokes equations are currently under development. The adjoint solution is used for dual-weighted error estimation. Using the lift or drag as a target functional, the sensitivity within the domain is determined. This solution is then used to weigh the local residual and determine the local error contribution with respect to the quantity of interest (Cl or Cd). The local error estimate then drives a p-adaptive algorithm to locally improve the local approximation order.