HYDRA is a suite of CFD programs being developed in conjunction with Rolls-Royce.
The initial research and development was carried out in our group over the period
1998-2002, but the further development now involves Rolls-Royce funded university
research groups at Cambridge, Imperial College, Loughborough, Surrey and Sussex.
HYDRA consists of four main codes:
- hyd to solve the nonlinear, steady or unsteady, flow equations.
- hydlin to solve the harmonic flow equations corresponding to linearised
unsteady flow at a given frequency.
- hydadj to solve the steady adjoint flow equations for steady-state
design optimisation.
- hydadjh to solve the adjoint harmonic flow equations, for certain flutter
and forced response design applications.
The linear code hydlin is obtained by linearising the discrete flow
equations in the nonlinear code hyd, and the adjoint codes are obtained
by transposing these equations appropriately. This corresponds to what is sometimes
referred to as the "fully-discrete" approach, as opposed to the "continuous" approach
in which the linearisation and adjoint formulation is performed at the PDE level.
Because of this approach, all four codes share a number of common features:
- choice of Euler equations or Navier-Stokes equations with Spalart-Allmaras
turbulence model
- use of hybrid unstructured grids comprising a collection of tetrahedra,
pyramids, prisms and hexahedra in 3D, or triangles and quadrilaterals in 2D
- multigrid solution with pseudo-time-marching and a Jacobi preconditioner
- distributed-memory parallel computation using the
OPlus parallel framework
- use of
Visual3 and
pV3
for visualisation
In the references below, [1] covers the research on the multigrid and
preconditioning and [2,8] explain the formulation and use of the harmonic adjoint
solution. Paper [3] contains our main contributions on the formulation and
solution of the adjoint equations, in particular the "fiully-discrete" approach,
the complexities introduced by the imposition of strong boundary conditions, and
the adjoint iterative approach to solving the adjoint equations.
Papers [4,5,7] address an important problem that arose with both the linear and
adjoint solvers. In situations where the nonlinear calculation had failed
to converge properly, and had instead settled into a low level limit cycle
oscillation, it was observed that the linear and adjoint calculatiosn would
be unstable, with the unstable eigenmode being localised in the region affected
by the nonlinear limit cycle. Sergio Campobasso found that a good way to
stabilise such calculations was to wrap a GMRES or RPM iteration around the
standard multigrid solver, using the multigrid solver as a preconditioner for
the outer GMRES or RPM solver. This has been very effective in solving what
was otherwise becoming an increasingly troublesome problem in 3D viscous
applications.
References
- P. Moinier, J.-D. Muller and M.B. Giles.
`Edge-based multigrid and preconditioning for hybrid grids'.
AIAA Journal, 40(10):1954-1960, 2002.
(PDF).
- M.C. Duta, M.B. Giles and M.S. Campobasso.
`The harmonic adjoint approach to unsteady turbomachinery design'.
International Journal for Numerical Methods in Fluids,
40(3-4):323-332, 2002.
(PDF file: 108kb).
- M.B. Giles, M.C. Duta, J.-D. Muller and N.A. Pierce.
`Algorithm developments for discrete adjoint methods'.
AIAA Journal, 41(2), 2003.
(PDF).
- M.S. Campobasso and M.B. Giles.
`Stabilization of a linearized Navier-Stokes solver for turbomachinery
aeroelasticity' in Computational Fluid Dynamics 2002.
Springer-Verlag, 2003.
(PDF).
- M.S. Campobasso and M.B. Giles.
`Effect of flow instabilities on the linear analysis of
turbomachinery aeroelasticity',
AIAA Journal of Propulsion and Power, 19(2), 2003
(PDF).
- M.S. Campobasso, M.C. Duta and M.B. Giles.
`Adjoint calculation of sensitivities of turbomachinery objective
functions', AIAA Journal of Propulsion and Power, 19(4), 2003.
(PDF).
- M.S. Campobasso and M.B. Giles.
`Stabilization of a linear flow solver for turbomachinery aeroelasticity
by means of the recursive projection method',
AIAA Journal, 42(9) 1765-1774, 2004.
(PDF).
- M.C. Duta, M.S. Campobasso, M.B. Giles and L.B. Lapworth.
`Adjoint harmonic sensitivities for forced response minimisation',
to appear in the ASME Journal of Turbomachinery, 2005.
- P. Moinier and M.B. Giles.
`Eigenmode analysis for turbomachinery applications',
to appear in AIAA Journal of Propulsion and Power, 2005.
(PDF).