Numerical Simulation of Weak Shock Wave Reflection in Water Media

Abstract Shock wave reflection (SWR) is an interesting physical phenomenon that plays an important role in the ocean engineering. The existing research mainly focused on the gas SWR. Compared with the gas SWR, the water SWR has distinctive features. This article uses numerical methods to study the reflection mode and regularity inside a gas-filled and water-filled wedge. Specifically, we use the fifth-order weighted essentially nonoscillatory method in space and the third-order Runge–Kutta (RK) method in time to solve the compressible Euler equations. The ideal gas equation of state and water equation of state are also considered in the simulations. We developed a numerical solver using the Fortran language based on these equations and numerical methods. The reliability and accuracy of the developed program were validated by the existing theoretical solution and experiment data. Results show that the reflections are different in gas and water media. Regular reflection (RR) and Mach reflection are observed in a gas-filled wedge. However, only the RR is observed in a water-filled wedge for the weak water shock. Besides, it is found that the reflected shock (RS) wave in water is straighter than that in gas medium. Under the same pressure condition, the curvature of the RS wave is larger in a gas medium. The difference in SWR mode can be attributed to the difference in compressibility between the gas and water. It is found that there is a significant increase in temperature behind the incidence shock in the gas due to its high compressibility, which causes the change of local wave speed especially near the reflected wave. However, the temperature and wave speed are approximately constant during the SWR process in water. These distinctions can well explain the difference in SWR modes between gas and water.