Multi-domain simulations of shock wave interaction with aerodynamic obstacles in cylindrical implosions

A multi-domain finite-volume approach is presented to simulate the interaction of converging shock waves and aerodynamic obstacles for dilute gases. The so-called reshaping process, in which the cylindrical shock is reshaped into a polygonal shock due to the presence of obstacles along the shock path, is studied. To accurately capture the diverse spatial scales of the problem, the computational domain is divided into three sub-domains, namely, the far-field region, the obstacle region and the focus region. Shock propagation in the far-field region is simulated under the axisymmetric, namely, one-dimensional approximation. The obstacle region is described by a fully two-dimensional model, in which initial conditions are interpolated from the far-field. The solution in the obstacle region is then interpolated into the focus region surrounding the center of the imploding shock. These two regions partially overlap to allow for linear interpolation. Numerical results are presented for air in dilute conditions and for four, eight, sixteen and twenty four aerodynamic obstacles. The proposed multi-domain solution technique is found to be capable of describing the complex gas dynamics of the shock propagation and reshaping, while reducing the computational burden for a large number of obstacles of one order of magnitude with respect to fully two-dimensional simulations.