*CABARET is a general-purpose advection scheme which is suited for computational aeronautics and geophysics
problems. For solving Navier-Stokes equations with Reynolds numbers of 10 ^{4}, the method gives a very good convergence without any additional preconditioning down to Mach numbers as low as 0.05-0.1. In particular for the MILES modelling of a hydrodynamic instability and free jet, a 257^{2} grid using CABARET is able to produce results comparable to a conventional second order method which would require at least 1025^{2} grid points [5]. Here, the CABARET method is 30 times more efficient.
*

*For linear advection, the CABARET scheme is a modification of the non-dissipative and low-dispersive Second-order Upwind Leapfrog method [6]. The modification consists of introducing separate conservation and flux variables that are staggered in space and time this results in a very compact, one cell in space and time computational stencil. In comparison to the standard finite-difference and finite-volume methods, in CABARET there is always an additional independent evolutionary variable, which gives the method the ability to preserve one more important property of the governing equations - the small phase and amplitude error. Traditionally conservation fluxes are computed at cell faces using cell-centre variable interpolation but with CABARET the conservation fluxes explicitly depend on the evolution of cell-centre and cell-face variables. 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.
*

*The key role of the nonlinear correction in the MILES CABARET method is to remove the under-resolved fine scales from the solution so that an accurate balance between the numerical dissipation and dispersion errors is preserved. For the Navier-Stokes equations, each time iteration of the CABARET method consists of a conservation phase and a characteristic decomposition phase.
*

Phil Ridley 2011-02-01