A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed spherically-symmetric flows of gas dynamics

Jean-Marie Clarisse (1)

1 DAM/DIF - DAM Île-de-France

An explicit Godunov-type method in Lagrangian coordinates is devised for computing three-dimensional linear perturbations about spherical radial flows of gas dynamics. This method relying on a description of the perturbed flow in terms of linear Lagrangian perturbations is an outgrowth of an unpublished work by the author (Clarisse, 2001) and of the Godunov-type method for multi-material flows in planar symmetry presented in (Clarisse et al., 2004). The principle of a discrete formulation of the geometric conservation law (Thomas 1979) for the motion perturbation is introduced, granting mass conservation at the perturbation level. A practical time-step constraint for the numerical stability of the linear perturbation computation is provided in the case of third-order non-degenerate Runge-Kutta schemes. The scheme numerical capabilities at producing reliable accurate results are demonstrated by computing free-surface deformations of a shell in homogeneous compression and front deformations of a self-similar converging spherical shock wave. The interest of such a perturbation computation approach in hydrodynamic stability studies is examplified in the latter case by obtaining shock-front deformation dynamics results having no precedents with respect to accuracy and perturbation wavelength range.

Keywords: Gas dynamics; linear hydrodynamic stability; Lagrangian perturbation; curvilinear coordinates; Godunov-type method; simple Riemann solver; geometric conservation law; Rayleigh-Taylor instability; converging spherical shock-wave stability

Domains: Fluid mechanics [physics.class-ph]

Jean-Marie Clarisse. A Godunov-type method in Lagrangian coordinates for computing linearly-perturbed spherically-symmetric flows of gas dynamics. 2007. ⟨hal-00197498⟩