A Numerical Study of a Converging Cylindrical Shock (Classic Reprint)

Numerical study of a converging cylindrical shock shows how a careful scheme can capture sharp shock fronts.

The report explains a practical approach to solving the one‑dimensional gas dynamics equations in Cartesian coordinates, while using operator splitting and Glimm’s method to keep shocks and contact discontinuities perfectly sharp.

Readers will see how random sampling and Riemann problems are used to advance the solution, how boundary conditions at the axis are handled, and how the converging shock strengthens and reflects as it approaches the axis. The work also discusses the accompanying ordinary differential equations solved with a simple Euler step and reports on computational requirements and visualization of results.

• How Glimm’s scheme solves Riemann problems exactly and efficiently for shock-dominated flows
• How axis boundary conditions are applied in a cylindrical setting
• What happens to pressure, velocity, density, and energy as a converging shock evolves and reflects
• What the figures and numerical details reveal about the method’s accuracy and behavior

Ideal for readers of computational fluid dynamics and numerical methods who want a concrete example of shock tracking in a converging geometry.