Application Overview

CABARET is a general-purpose advection scheme which is suited for computational aeronautics and geophysics problems [1]. For solving Navier-Stokes equations with Reynolds numbers of 10000, the method gives a very good convergence without any additional preconditioning down to Mach numbers as low as 0.05. In particular for the modelling of a hydrodynamic instability and free jet, CABARET is able to produce results comparable to a conventional second order method with at least 30 times more efficiency [2]. The CABARET method is a low dissipative and low dispersive scheme that constitutes a substantial upgrade of the second-order upwind leapfrog. The algorithm is very suitable for distributed HPC since it has a very local computational stencil that for scalar advection constitutes only one cell in space and time.

For this project, two very important CFD applications which both use CABARET will be optimised for improved performance on HPC architectures: one of which is for modelling aircraft jet engine-flap interaction community noise, and the other for modelling transient mesoscale eddies of the ocean circulation.

The ocean circulation problem is important, because the ocean contributes to the climate variability, and this contribution is largely controlled and even driven by the intrinsic nonlinear dynamics associated with the mesoscale eddies. Some of the corresponding eddy effects are non-diffusive and even anti-diffusive, implying that they are very difficult to parameterize in a simple way. The inability to resolve the eddies dynamically is a major hurdle for predictive understanding of the global climate variability.

Resolving the eddies is a high-priority task, which requires cutting-edge numerical models coupled with supercomputing resource. The Parallel Quasi-Geostrophic Model (PEQUOD) code is a leading application in this area and has been developed to solve the layered quasi-geostrophic potential vorticity equation [3]-[4] subject to forcing and dissipation. The use of an optimised version of PEQUOD on HECToR will enable unprecedented levels of the dynamical realism and structural details of the eddies and their effects on the large-scale ocean circulation. This, in turn, will be an important contribution to climate research, by enabling calculations for the most turbulent and, thus, the most physically relevant regimes of the ocean circulation, in the classical quasigeostrophic set up:

  1. Intrinsic large-scale low-frequency variability of the turbulent wind-driven ocean gyres;
  2. Physics of the eddy/large-scale flow interactions maintaining large-scale circulation and its variability;
  3. Material transport induced by the mesoscale oceanic eddies;
  4. Parameterisation of the essential eddy effects for use in oceanic components of comprehensive global-climate models.

Also as important is the aircraft noise problem, because by 2020 the total number of flights is expected to double and, accordingly, each individual aircraft needs to be made at least twice as quiet. In the past, jet noise reduction for civil aircraft could be achieved by increasing the size of the jet engines. This allows a reduction of the jet speed for the same amount of thrust and, since jet noise scales as a high power of the jet exit velocity, this also reduces the noise. However, any further decrease is only possible if detailed noise mechanisms are quantified and jet noise reduction remains a formidable problem.

In addition to the jet noise problem, the airframe noise including the airframe/engine interaction effects is a major contributor to the aircraft noise at approach and its reduction also becomes a problem [5]-[6]. In particular, when deployed at a large angle of attack at approach conditions, the flaps become a dominant noise source for the airframe noise. Moreover, for engine-under-a-wing configurations, Jet-Flap Interaction (JFI) noise can also become an important noise component at take-off conditions.

For flight conditions such effects are often coupled, which makes high-resolution computational modelling ever more valuable. The complexity of the unsteady flow sets the minimum size of the computational problem that aims to model it has to be extremely large. But by using the high-resolution Cfoam-CABARET code and extending it to large-scale models on HECToR, the important unsteady effects of flap-jet interaction that contribute to noise can then be captured. Cfoam-CABARET uses a Monotonically Integrated LES (MILES) approach to the solution of the Navier-stokes equations. For enforcing the non-oscillatory property of the solution, the CABARET scheme uses a low-dissipative non-linear flux correction that is directly based on the maximum principle for the flux variables. Each time iteration of the method then consists of a conservation phase and a characteristic decomposition phase.

Phil Ridley 2012-10-01