Paper 14: Numerical Solutions of Flows behind Shock Waves in Non-Uniform Regions

Abstract

Different computational schemes for the calculation of multi-dimensional non-stationary problems of gas dynamics with shock waves present are reviewed. A differencing scheme developed in the last few years at the Los Alamos Scientific Laboratory, known as the ‘fluid-in-cell’ method, has been employed to obtain numerical solutions for the time-dependent two-dimensional flows initiated by the passage of a shock wave in a duct with either a gradual or sudden change in cross-section and in a branched duct. The numerical results have been displayed in the form of contours of density, pressure, and internal energy. The main features of the computed solutions have been compared with the experimental flow patterns obtained by the authors. Comparison of pressure–time records shows good agreement. The fluid-in-cell method is well suited for machine calculation on a high-speed electronic computer and can treat unsteady two-dimensional compressible flow problems involving a single material within closed boundaries, without excessive demands on storage and computing time.