Embedded Boundary Algorithms for Solving the Poisson Equation on Complex Domains

Day, Marcus S.; Colella, Phillip; Lijewski, Michael J.; Rendleman, Charles A.; Marcus, Daniel L.

doi:10.2172/771633

Cited by 20 publications

(17 citation statements)

References 8 publications

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“…On a uniform grid without solid boundaries, the approach presented reduces to the approximate projection method described by Martin [21,22]. Solid boundaries are treated using a combination of a Poisson solver similar to the one studied by Johansen and Colella [23,24] and of a cell-merging technique for the advection scheme [14]. In contrast to classical AMR strategies, adaptive refinement is performed at the fractional timestep.…”

Section: Preprint Submitted To Journal Of Computational Physicsmentioning

confidence: 99%

Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Popinet

2003

Journal of Computational Physics

1,069

862

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An adaptive mesh projection method for the time-dependent incompressible Euler equations is presented. The domain is spatially discretised using quad/octrees and a multilevel Poisson solver is used to obtain the pressure. Complex solid boundaries are represented using a volume-of-fluid approach. Second-order convergence in space and time is demonstrated on regular, statically and dynamically refined grids. The quad/octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features. The source code of the method implementation is freely available.

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Section: Preprint Submitted To Journal Of Computational Physicsmentioning

confidence: 99%

Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Popinet

2003

Journal of Computational Physics

1,069

862

View full text Add to dashboard Cite

show abstract

“…Our pressure discretization effectively ignores any dangling interior solid faces arising from partially cut cells, as in previous regular grid schemes for thin boundaries (e.g., (DAY et al, 1998;GUENDELMAN et al, 2005; ROBINSON-MOSHER; ENGLISH; FEDKIW, 2009)).…”

Section: Dangling Cut-cellsmentioning

confidence: 99%

“…Our pressure discretization ignores dangling interior solid faces arising from partially cut cells, as in previous regular grid schemes for thin boundaries (e.g., (DAY et al, 1998;GUENDELMAN et al, 2005;FEDKIW, 2009)). Precisely accounting for this geometry would require generating a fully unstructured conforming mesh within the cell.…”

Section: Limitationsmentioning

confidence: 99%

Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

2016

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Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.

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“…Interfaces, sharp angles or even thin bodies restrict the efficiency of methods that rely on multigrid solvers, see e.g. [24]. More recently, [55] noted that high frequency fields need to be smeared out in order to alleviate convergence problems, and pointed out that high order schemes have less favorable smoothing properties than low order schemes forcing them to use a combination of low and high order to achieve both reasonable accuracy and convergence.…”

Section: Free Surface Flow On Octreesmentioning

confidence: 99%

Economic Analysis of National Nuclear Security Administration (NNSA) Modernization Alternatives

Hunter¹,

Bittle²,

Celec³

et al. 2007

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Since the seminal work of [92] on coupling the level set method of [69] to the equations for two-phase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interestingly, this work also demonstrated the largest weakness of the level set method, i.e. mass or information loss characteristic of most Eulerian capturing techniques. In fact, [92] introduced a partial differential equation for battling this weakness, without which their work would not have been possible. In this paper, we discuss both historical and most recent works focused on improving the computational accuracy of the level set method focusing in part on applications related to incompressible flow due to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical methods such as Hamilton-Jacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27]

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Embedded Boundary Algorithms for Solving the Poisson Equation on Complex Domains

Cited by 20 publications

References 8 publications

Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries

Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

Economic Analysis of National Nuclear Security Administration (NNSA) Modernization Alternatives

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