Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian–Eulerian methods

Berndt, Markus; Breil, J.; Galera, Stéphane; Kuchařík, Milan; Maire, Pierre‐Henri; Shashkov, Mikhail

doi:10.1016/j.jcp.2011.05.003

Cited by 75 publications

(57 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Instead, we treat interpolated values as target values and conservatively remap values in overlapped regions. This is similar in spirit to [37,47,46,45,9]. The spatially contiguous target values are defined on the Voronoi mesh and created by applying the pressure fluxes specified in Equations 26 and 28 as well as the high order diffusion specified in Equation 36.…”

Section: Conservationmentioning

confidence: 99%

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

Qiu

Fedkiw

2016

Journal of Computational Physics

View full text Add to dashboard Cite

We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.

show abstract

Section: Conservationmentioning

confidence: 99%

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

Qiu

Fedkiw

2016

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Note that a typical semi-Lagrangian method also has no mechanism to account for this dilation and therefore would possess similar errors. Those who pursue the semi-Lagrangian approach through a Lagrangian plus remap-style method can account for dilation and volume changes, and although significantly more complex than our approach, they bear some similarities; see for example [6] and the references therein.…”

Section: Non-uniform Gridsmentioning

confidence: 99%

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

Gretarsson

Fedkiw

2013

Journal of Computational Physics

View full text Add to dashboard Cite

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.

show abstract

“…The exact ratio of the computational cost of both methods is implementation dependent. In, the swept‐based method was shown to be approximately two times faster than intersections on a staggered mesh. Similar results with even higher ratios were published also in .…”

Section: Introductionmentioning

confidence: 99%

Combined swept region and intersection‐based single‐material remapping method

Klima

Kuchařík

Shashkov

2017

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

Summary A typical arbitrary Lagrangian–Eulerian algorithm consists of a Lagrangian step, where the computational mesh moves with the fluid flow; a rezoning step, where the computational mesh is smoothed and repaired in case it gets too distorted; and a remapping step, where all fluid quantities are conservatively interpolated on this new mesh. In single‐material simulations, the remapping process can be represented in a flux form, with fluxes approximated by integrating a reconstructed function over intersections of neighboring computational cells on the original and rezoned computational mesh. This algorithm is complex and computationally demanding – Therefore, a simpler approach that utilizes regions swept by the cell edges during rezoning is often used in practice. However, it has been observed that such simplification can lead to distortion of the solution symmetry, especially when the mesh movement is not bound by such symmetry. For this reason, we propose an algorithm combining both approaches in a similar way that was proposed for multi‐material remapping (two‐step hybrid remap). Intersections and exact integration are employed only in certain parts of the computational mesh, marked by a switching function – Various different criteria are presented in this paper. The swept‐based method is used elsewhere in areas that are not marked. This way, our algorithm can retain the beneficial symmetry‐preserving capabilities of intersection‐based remapping while keeping the overall computational cost moderate.

show abstract

Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian–Eulerian methods

Cited by 75 publications

References 42 publications

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

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

Combined swept region and intersection‐based single‐material remapping method

Contact Info

Product

Resources

About