Consistent mass and momentum transport for simulating incompressible interfacial flows with large density ratios using the level set method. (English) Zbl 1365.76238
Summary: There exists a sharp density jump at the fluid interfaces in most of interfacial flows encountered in engineering applications. Numerical treatment of the discontinuous fluid density in such flows is a great challenge. In particular, numerical errors can lead to non-physical results at large density ratios, hence limit a flow solver to only small and usually unrealistic density ratios. We introduce a consistent mass and momentum transport method which allows for simulations of interfacial flows with large density ratios in the context of the level set method. Fluid momentum is transported by discretizing the conservative form of the convective term in the momentum equation. A new technique is introduced to compute the flux density based on the temporal evolution of the fluid interfaces and by using the level set function at two subsequent time levels. For consistency, we use the same flux density for both mass and momentum transport, and thereby establish a tight coupling between them. We assess the performance of the proposed method by using a set of benchmark test cases, in which the density ratio ranges from 650 to 10\(^6\). The new method is stable and accurate even at extreme density ratios. The numerical results agree very well with the theoretical and experimental results. In contrast, the results of a non-conservative formulation show non-physical fluid behavior, where the dense fluid is slowed down by the light fluid due to numerical errors.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76D99 | Incompressible viscous fluids |
Keywords:
level set; interfacial flows; two-phase flows; large density ratio; sheet breakup; atomizationReferences:
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