Viscous flow past a cylinder close to a free surface: Benchmarks with steady, periodic and metastable responses, solved by meshfree and mesh-based schemes

Resumen

The question of whether it is possible to set relevant, robust and reliable benchmarks for viscous free surface flows with complex free-surface dynamics is investigated in this work. The proposed method for finding an answer to this question consists of selecting three conditions leading to increasing flow complexity and to simulate them using three well established solvers based on diverse numerical techniques. In the three conditions, a submerged horizontal cylinder in an uniform current perpendicular to its axis is considered, the Reynolds number is fixed to 180, and the analysis is limited to a 2D framework. While the unbounded solution for such flow is well established, adding a free surface and setting the submergence ratio and the Froude number in certain ranges, challenging free-surface dynamics takes place. In the specific conditions selected, phenomena of increasing complexity are identified and studied with: (i) delta(+)-SPH, an enhanced version of the Smoothed Particle Hydrodynamics method, (ii) a single-phase Finite Volume scheme with a Level Set function for tracking the free-surface (LS-FVM), and (iii) a two-phase Finite Volume with a Volume-of-Fluid algorithm to treat the gas/liquid interface (VOF-FVM). It is shown that the test-cases, even being geometrically simple, present intricate complexities, such as alternate metastable states in the wake, linked to the strong non-linearities induced by the interactions between the wake's vorticity and the free surface. It is also shown that the solvers considered are able to depict a consistent representation of these complex flows, useful as benchmarks for other solvers and methods. An additional research question, investigating whether the improvements of the delta(+) variant of the SPH method are necessary for simulating specific aspects of the flows treated in the paper, is also posed and discussed.