Weighted Essentially Non-Oscillatory Simulations and Modeling of Complex Hydrodynamic Flows. Part 1. Regular Shock Refraction

摘要

Shock refraction is a fundamental shock phenomenon observed when shocks interact with a material interface separating gases with different properties. Following refraction, a transmitted shock enters the second gas and a reflected wave returns back into the first gas. In the case of regular shock refraction, all of the waves meet at a single point called the triple-point, creating five different states for the two gases. Analytical methods based on shock polar analysis have been developed to determine the state of two ideal gases in each of the five refraction regions. Furthermore, shock refraction constitutes a basic example of complex hydrodynamic flows. For this reason, shock refraction is used in this report as one validation of the high-order accurate weighted essentially non-oscillatory (WENO) shock-capturing method, as implemented in the HOPE code. The algorithms used in the HOPE code are described in detail, together with its current capabilities. The following two-step validation process is adopted. First, analytical results are obtained for the normal and oblique shock refraction (with shock-interface angle {beta}{sub interface} = 75{sup o}) observed for a Ma = 1.2 shock. To validate the single-fluid and the two-fluid implementations of the WENO method, two pairs of gases, argon/xenon, having equal adiabatic exponents {gamma} and air(acetone)/sulfur hexafluoride, having different adiabatic exponents, are considered. Both the light-to-heavy and heavy-to-light gas configurations are considered. Second, numerical simulations are performed using the fifth-order WENO method and values of the density, pressure, temperature, speed of sound, and flow velocity in each of the five refraction regions are compared with the analytical predictions obtained from shock polar analysis. In all of the cases considered, excellent agreement is found between the simulation results and the analytical predictions. The results from this investigation suggest that the WENO method is a very useful numerical method for the simulation and modeling of complex hydrodynamic flows.