A parameter-free total Lagrangian smooth particle hydrodynamics algorithm applied to problems with free surfaces

This paper presents a new Smooth Particle Hydrodynamics computational framework for the solution of inviscid free surface flow problems. The formulation is based on the Total Lagrangian description of a system of first-order conservation laws written in terms of the linear momentum and the Jacobian of the deformation. One of the aims of this paper is to explore the use of Total Lagrangian description in the case of large deformations but without topological changes. In this case, the evaluation of spatial integrals is carried out with respect to the initial undeformed configuration, yielding an extremely efficient formulation where the need for continuous particle neighbouring search is completely circumvented. To guarantee stability from the SPH discretisation point of view, consistently derived Riemann-based numerical dissipation is suitably introduced where global numerical entropy production is demonstrated via a novel technique in terms of the time rate of the Hamiltonian of the system. Since the kernel derivatives presented in this work are fixed in the reference configuration, the non-physical clumping mechanism is completely removed. To fulfil conservation of the global angular momentum, a posteriori (least-squares) projection procedure is introduced. Finally, a wide spectrum of dedicated prototype problems is thoroughly examined. Through these tests, the SPH methodology overcomes by construction a number of persistent numerical drawbacks (e.g. hour-glassing, pressure instability, global conservation and/or completeness issues) commonly found in SPH literature, without resorting to the use of any ad-hoc user-defined artificial stabilisation parameters. Crucially, the overall SPH algorithm yields equal second order of convergence for both velocities and pressure

Instabilities of flow in a corrugated pipe

Flow in a corrugated pipe is considered. Different from previous studies. both the corrugation amplitude and wavelength are much smaller than the pipe diameter. Results of the multi-scale analysis show that the mean flow modulated by the surface corrugation becomes unstable to three-dimensional travelling waves at moderate Reynolds numbers, and the wave with one azimuthal period is found to be the most unstable mode.Engineering, MechanicalMechanicsEICPCI-S(ISTP)

Maximum growth of Gortler vortices

International audienceThis study is concerned with the numerical calculation of the maximum spatial growth of Gortler vortices on a concave wall. The method is based on the direct computation of a discrete approximation to the spatial propagator that relates the downstream response to the inlet perturbation. The optimization problem is then solved directly by making use of the propagator matrix. The inlet optimal perturbations and the outlet optimal response that are found are similar to those found with the same measure by Andersson et al. [1] and Luchini [5] in the case of the boundary layer on a flat plate. The study of a simple "toy" model problem suggests that the streamwise evolution of perturbations is essentially determined by the non-normality of the spatial propagator