Abstract
A second-order accurate difference scheme is developed to study cavitation in unsteady, one-dimensional, inviscid, compressible flows of water with gas. The scheme can capture shock waves, interfaces separating gas and water, as well as cavitation zones that are modelled as vacuum states, and it takes into account water's capability to resist tensile stresses. As an extended version of the standard MUSCL scheme, this scheme is based on the solutions of local gas–water–vacuum initial value problems. In order to prevent the computed water density from becoming lower than its minimum bound, additional techniques are introduced. Numerical results are presented with gas–water Riemann problems to demonstrate the performance of the scheme. The scheme is also applied to simulate the cavitation process of the flow in a water shock tube.
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