Sharp-interface method for compressible flow

One way to deal with compressible multi-fluid flow is the levels-set method. We define an interface dividing our computational domain in two sub-domains, each of which corresponding to one fluid. We introduce a signed distance function called the level set function whose zero value indicates the interface. Different fluids are identified with opposite signs of the level-set function.

Continuous updating of the level-set is equivalent to the advection of the interface with the flow-field]. In practice, the level-set is updated in the near interface region, while the field is re-initialized far away of the interface in order to obtain a smooth signed distance function.

Identifying the interface between two fluids by the zero-level-set allows a sharp interface representation and an accurate computation of volume fractions in any computational cell cut by the interface. This is a basic requirement for our conservative multi-phase model.

We use the compressible level-set method to simulate compressible multi-phase problems. After identifying the interface between two fluids and computing the volume fractions and face apertures in cells cut by the interface, both flow fields are calculated independently. The only dependencies are the interface interactions which we combine in a conservative exchange term added to the right-hand side of the transport equations. The interactions across the interface are calculated by a Riemann-solver [1]. For cells with small volume fractions stability might not be obtained based on the time step calculated according to the full grid size CFL condition. Therefore we mix those cells with neighbor cells in a conservative way [2]. Due to our fully conservative approach, we ensure mass conservation down to the resolution limit. Unresolved mass is deleted automatically.

Introducing an additional evaporation model, we are able to model phase change, like it occurs in flows with cavitation[4].

Fig.1 Sample levelset field. The black line indicates the interface.

Selected Publications:

Hu X.Y., Khoo B.C., An interface interaction method for compressible multifluids, J. Comp. Phys. 198 (2004) 35-64.
Hu X.Y., Khoo B.C., Adams N.A., Huang F.L., A conservative interface method for compressible flows, J. Comp. Phys. 219 (2006) 553-578.
Hu X.Y., Adams N.A., Johnson E., Iaccarino G., Modeling full-Mach-range cavitating flow with sharp interface model, In Proceedings of the 2008 Summer Program, CTR, Stanford, CA, July 6 - August 1 (2008).