Two-Phase Compressible Flow

Abstract

Chronologically, the first attempt to use the level set method for flows involving external physics was in the area of two-phase inviscid compressible flow. Mulder et al. [115] appended the level set equation (15.1) to the standard equations for one-phase compressible flow, equation (14.47). Here V is taken to be the velocity of the compressible flow field, so that the zero level set of ¢ corresponds to particle velocities and can be used to track an interface separating two different compressible fluids. The sign of ¢ is used to identify which gas occupied which region, i.e., to determine the local equation of state. In [115], only gamma law gas models were considered, with I = 11 for ¢ > 0 and I = 12 for ¢ S o. Later, Karni [93J pointed out that this method suffered from spurious oscillations at the interface. Figure 15.1 shows a sample calculation using the method proposed in [115]. Here a right going shock wave impinges upon the interface, producing both reflected and transmitted shock waves. Note the spurious oscillations in both the pressure and the velocity profiles near the centrally located contact discontinuity that separates the two different gamma-law gases. S. Osher et al., Level Set Methods and Dynamic Implicit Surfaces