A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics

Understand

The nonlinear evolution of the Kelvin-Helmholtz instability is a popular test for code verification.

• To date, most Kelvin-Helmholtz problems discussed in the literature are ill-posed: they do not converge to any single solution with increasing resolution.
• This precludes comparisons among different codes and severely limits the utility of the Kelvin-Helmholtz instability as a test problem.
• The lack of a reference solution has led various authors to assert the accuracy of their simulations based on ad-hoc proxies, e.g., the existence of small-scale structures.