An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A 367, no. 1907, 4559-4575 (2009, the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of "standard fluxes" from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Many diffuse immersed boundary methods used in recent literature employ artificial volume forces distributed over a zone of cells close to the interface to effectively represent the pressure force exerted by the immersed boundary. This stress can be distributed to the surrounding fluid using, for example, a dirac delta function, a distributed function or a forcing term. Early examples can be found in [4][5][6][7]. The advantage of this approach is that the wall geometry appears only in the distributed momentum forces, while the surface geometry does not otherwise affect the scheme. In particular, intersections of the wall geometry with computational cells do not have to be accounted for explicitly. Recent developments using this approach include particle flow applications [8,9] and heat transfer applications [10,11].Another popular class of diffuse boundary methods are the "fictitious domain" methods. In this approach, both fluid and solid regions are treated mathematically as a fluid, with either a material-dependent rigidity constraint, as in Glowinski et al. [12], or the fluid and solid regions are treated as a porous medium, using the Navier Stokes/Brinkmann equations with a permeability parameter-based forcing term, as in Angot et al. [13] and Khadra et al. [14]. Recent, notable developments to the fictitious domain approach include Randrianarivelo et al. [15], Angot [16]...

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NOMENCLATURE ABSTRACTThis work investigates the non-uniform total temperature and total pressure downstream of a circular cylinder in transonic flow. At Mach 0.6 shock induced separation of the flow occurs from the surface of the cylinder. The unsteady shear layers roll up into vortices that are shed from the cylinder forming a von Kármán vortex street of convecting vortices. An experimental investigation of the vortex street is carried out at a distance of six cylinder diameters downstream. Time resolved total temperature measurements reveal the presence of localised 'hot spots' of increased total temperature at the edges of the wake and localised * Research Student.'cold spots' of decreased total temperature along the centre of the wake. The experimental measurements are compared against a concurrent numerical study using a time accurate numerical model with turbulence closure. The numerical model also captures the nonuniform total temperature and total pressure distribution downstream of the cylinder. The non-uniform total temperature and total pressure distribution is shown to be a source of entropy production. Comparison of the total temperature and total pressure distribution highlights the influence of the boundary layer development and separation characteristics on the vortex shedding and energy separation processes. This emphasizes the importance of including the effects of turbulence and boundary layer development in numerical studies of the energy separation downstream of circular cylinders.

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