SUMMARYA Hermitian-Fourier numerical method for solving the Navier-Stokes equations with one non-homogeneous direction had been presented by Schiestel and Viazzo (Internat. J. Comput. Fluids 1995; 24(6):739). In the present paper, an extension of the method is devised for solving problems with two non-homogeneous directions. This extension is indeed not trivial since new algorithms will be necessary, in particular for pressure calculation. The method uses Hermitian ÿnite di erences in the non-periodic directions whereas Fourier pseudo-spectral developments are used in the remaining periodic direction. Pressure-velocity coupling is solved by a simpliÿed Poisson equation for the pressure correction using direct method of solution that preserves Hermitian accuracy for pressure. The turbulent ow after a backward facing step has been used as a test case to show the capabilities of the method. The applications in view are mainly concerning the numerical simulation of turbulent and transitional ows.

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This paper describes a 3-stage technique to model the propagation to the far field of nonlinear shock waves produced by high-energy explosive sources. The stages are: (1) a 3-dimensional unsteady Euler method for the strong shock near the source, including a Flux-Corrected-Transport (FCT) method, (2) the Nonlinear Progressive-wave Equation (NPE) procedure for the degeneration of the shock into a linear acoustical wave, and (3) the Parabolic Equation (PE) method for propagation to the far field. Comparisons of calculated data with a linear analytical method are shown. © 2005 Institute of Noise Control Engineering.

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A numerical method for calculating strong shock waves generated by large guns is presented. The method is based on numerical simulations of the time-dependent flow field of a muzzle blast wave, in the regions inside and near the muzzle of the gun. The objective of this work is to numerically investigate possible means of mitigation of the pressure waves with obstacles or absorbing materials placed in the vicinity of the firing areas., by means of numerical solutions of the time dependent flow field in the region surrounding the gun. This paper presents the first stage of this research and focuses on the development and validation of the numerical method. © 2002 Institute of Noise Control Engineering.