An Adaptive Level Set Approach for Incompressible Two-Phase Flows

Sussman, Mark; Almgren, Ann S.; Bell, John B.; Colella, Phillip; Howell, Louis H.; Welcome, Michael

doi:10.1006/jcph.1998.6106

Cited by 559 publications

(212 citation statements)

References 39 publications

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“…In additions, adaptive framework have been introduced (see e.g. [138,15,3,14,143,76,51,19,137,10,92,4,111,41,25,58,128,66] and the references therein).…”

Section: Improvement On Mass Conservationmentioning

confidence: 99%

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High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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We present a review of some of the state-of-the-art numerical methods for solving the Stefan problem and the Poisson and the diffusion equations on irregular domains using (i) the level-set method for representing the (possibly moving) irregular domain's boundary, (ii) the ghost-fluid method for imposing the Dirichlet boundary condition at the irregular domain's boundary and (iii) a quadtree/octree nodebased adaptive mesh refinement for capturing small length scales while significantly reducing the memory and CPU footprint. In addition, we highlight common misconceptions and describe how to properly implement these methods. Numerical experiments illustrate quantitative and qualitative results.

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“…In additions, adaptive framework have been introduced (see e.g. [138,15,3,14,143,76,51,19,137,10,92,4,111,41,25,58,128,66] and the references therein).…”

Section: Improvement On Mass Conservationmentioning

confidence: 99%

“…Numerical methods for a large class of partial differential equations have been introduced using this framework; see e.g. [14,138,85] and the references therein. More recently, quadtree and octree data structures have been preferred [3], since they allow the grid to be continuously refined without being bound by blocks of uniform grids.…”

Section: Introductionmentioning

confidence: 99%

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

2012

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“…The most common fixed-mesh techniques are based on the volume of fluid (VOF) [23], the level set [24,25] and the interface-sharpening/global mass conservation (IS-GMC) methods [26,27]. In these methods, the Navier-Stokes equations are solved over a non-moving mesh.…”

Section: T Wan S Aliabadi and C Biglermentioning

confidence: 99%

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

Wan

Aliabadi

Bigler

2009

Numerical Methods in Fluids

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SUMMARYWe have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

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“…For contours this typically amounts to using quadtrees [6,21,39] and more recently this idea was extended to surfaces by means of octrees [16]. Furthermore, Milne [20] and Sussman et al [29] have explored level sets in conjunction with patch based AMR.…”

Section: Previous Workmentioning

confidence: 99%

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

Nielsen

Museth

2006

J Sci Comput

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Level set methods [Osher and Sethian. Fronts propagating with curvaturedependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79 (1988) 12] have proved very successful for interface tracking in many different areas of computational science. However, current level set methods are limited by a poor balance between computational efficiency and storage requirements. Tree-based methods have relatively slow access times, whereas narrow band schemes lead to very large memory footprints for high resolution interfaces. In this paper we present a level set scheme for which both computational complexity and storage requirements scale with the size of the interface. Our novel level set data structure and algorithms are fast, cache efficient and allow for a very low memory footprint when representing high resolution level sets. We use a time-dependent and interface adapting grid dubbed the "Dynamic Tubular Grid" or DT-Grid. Additionally, it has been optimized for advanced finite difference schemes currently employed in accurate level set computations. As a key feature of the DT-Grid, the associated interface propagations are not limited to any computational box and can expand freely. We present several numerical evaluations, including a level set simulation on a grid with an effective resolution of 1024 3 .

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An Adaptive Level Set Approach for Incompressible Two-Phase Flows

Cited by 559 publications

References 39 publications

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

High Resolution Sharp Computational Methods for Elliptic and Parabolic Problems in Complex Geometries

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

Dynamic Tubular Grid: An Efficient Data Structure and Algorithms for High Resolution Level Sets

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