A conservative level-set based method for compressible solid/fluid problems on fixed grids

Barton, Philip T.; Obadia, B.; Drikakis, Dimitris

doi:10.1016/j.jcp.2011.07.008

Cited by 83 publications

(52 citation statements)

References 28 publications

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“…We do not consider three spatial dimensions in this paper, and instead refer the interested reader to [4] or [45] where cut cell generation techniques are discussed.…”

Section: Computing Cut Cellsmentioning

confidence: 99%

“…Many of these works concern themselves with fluid flow in the incompressible flow regime, see for example [8,22] and the references within, but researchers are increasingly giving attention to the two-way coupled interactions that arise in compressible flows, see for example [4,17,9]. If one desires to use a stateof-the-art Eulerian method on the fluid flow, and a state-of-the-art Lagrangian method for the structure solver, then this requires a numerical method for coupling these two solvers together.…”

Section: Introductionmentioning

confidence: 99%

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Fully conservative leak-proof treatment of thin solid structures immersed in compressible fluids

Gretarsson

Fedkiw

2013

Journal of Computational Physics

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We propose a novel high resolution conservative advection scheme that is suitable for thin, embedded moving solid structures. The scheme works by coupling together a high order flux-based method with a conservative semi-Lagrangian solver that is similar in spirit to that of [26], but modified to treat the cut cells and partial volumes that arise near a thin solid structure. The conservative semi-Lagrangian scheme is unconditionally stable, and so unlike previous methods no cell merging is required to compensate for the small cell volumes that arise. Furthermore, as the semi-Lagrangian scheme works via tracing characteristic curves, no special treatment is required either to enforce non-penetration through thin, moving solid structures, or to populate swept or uncovered degrees of freedom. For the flux-based solver, we use finite-difference ENO with LaxFriedrich's diffusion (although any flux-based scheme works), and in doing so we found that a modification to the diffusion calculation leads to improved stability in its third order accurate variant. We integrate this novel hybrid advection scheme into a semi-implicit compressible flow solver, and modify the implicit pressure solver to work with cells of variable size. In addition, we propose an improvement to the semiimplicit compressible flow solver via a new method for computing a post-advected pressure. Finally, this hybrid conservative advection scheme is integrated into a semi-implicit fluid-structure solver, and a number of one-dimensional and two-dimensional examples are considered-in particular, showing that we can handle thin solid structures moving through the grid in a fully conservative manner, preventing fluid from leaking from one side of the structure to the other and without the need for cell merging or other special treatment of cut cells and partial volumes.

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“…We do not consider three spatial dimensions in this paper, and instead refer the interested reader to [4] or [45] where cut cell generation techniques are discussed.…”

Section: Computing Cut Cellsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fully conservative leak-proof treatment of thin solid structures immersed in compressible fluids

Gretarsson

Fedkiw

2013

Journal of Computational Physics

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“…Thus, the majority of the interface capturing techniques exhibit deficiencies in conserving the mass. Several recent studies have introduced novel techniques for alleviating this deficiency [5], [6], [7], [8], [9].…”

Section: Introductionmentioning

confidence: 99%

An embedded approach for immiscible multi‐fluid problems

Ryzhakov

Jarauta

2015

Numerical Methods in Fluids

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An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated and its potential applications are shown.

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“…However, the ghost cells only work when there are real fluid cells for them to interact with, and all the real fluid cells disappear when solids come into close contact. Similarly, methods such as [3,17,18,36] which rely on cut cells that are merged with full cells to avoid accuracy and time step restrictions also cannot be applied when all the full cells vanish as the solids come into close contact. Fictitious domain (see e.g.…”

Section: Introductionmentioning

confidence: 99%

On thin gaps between rigid bodies two-way coupled to incompressible flow

Qiu

Fedkiw

2015

Journal of Computational Physics

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Two-way solid fluid coupling techniques typically calculate fluid pressure forces that in turn drive the solid motion. However, when solids are in close proximity (e.g. touching or in contact), the fluid in the thin gap region between the solids is difficult to resolve with a background fluid grid. Although one might attempt to address this difficulty using an adaptive, body-fitted, or ALE fluid grid, the size of the fluid cells can shrink to zero as the bodies collide. The inability to apply pressure forces in a thin lubricated gap tends to make the solids stick together, since collision forces stop interpenetration but vanish when the solids are separating leaving the fluid pressure forces on the surface of the solid unbalanced in regards to the gap region. We address this problem by adding pressure degrees of freedom onto surfaces of rigid bodies, and subsequently using the resulting pressure forces to provide solid fluid coupling in the thin gap region. These pressure degrees of freedom readily resolve the tangential flow along the solid surface inside the gap and are two-way coupled to the pressure degrees of freedom on the grid allowing the fluid to freely flow into and out of the gap region. The two-way coupled system is formulated as a symmetric positive-definite matrix which is solved using the preconditioned conjugate gradient method. Additionally, we provide a mechanism for advecting tangential velocities on solid surfaces in the gap region by extending semi-Lagrangian advection onto a curved surface mesh where a codimension-one velocity field tangential to the surface is defined. We demonstrate the convergence of our method on a number of examples, such as underwater rigid body separation and collision in both two and three spatial dimensions where typical methods do not converge. Finally, we demonstrate that our method not only works for the aforementioned "wet" contact, but also works in conjunction with "dry" contact where there is no fluid in the gap between the solids.

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A conservative level-set based method for compressible solid/fluid problems on fixed grids

Cited by 83 publications

References 28 publications

Fully conservative leak-proof treatment of thin solid structures immersed in compressible fluids

Fully conservative leak-proof treatment of thin solid structures immersed in compressible fluids

An embedded approach for immiscible multi‐fluid problems

On thin gaps between rigid bodies two-way coupled to incompressible flow

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