The Introduction of Micro Cells to Treat Pressure in Free Surface Fluid Flow Problems

Raad, Peter E.; Chen, Shea; Johnson, David B.

doi:10.1115/1.2817323

Cited by 27 publications

(11 citation statements)

References 15 publications

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“…In this work we restrict ourselves to two-dimensional applications. Bi-linear interpolation functions are used in (12) for all elements that are not cut by the interface. In cut elements, however, we subdivide the quadrilateral element into two triangulars and employ linear interpolation functions.…”

Section: Description Of the Interfaces By The Level-set Methodsmentioning

confidence: 99%

The intrinsic XFEM for two‐fluid flows

Fries

2008

Numerical Methods in Fluids

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SUMMARYIn two-fluid flows, jumps and/or kinks along the interfaces are present in the resulting velocity and pressure fields. Standard methods require mesh manipulations with the aim that either element edges align with the interfaces or that the mesh is sufficiently refined near the interfaces. In contrast, enriched methods, such as the extended finite element method (XFEM), enable the representation of arbitrary jumps and kinks inside elements. Thereby, optimal convergence can be achieved for two-fluid flows with meshes that remain fixed throughout the simulation. In the intrinsic XFEM, in contrast to other enriched methods, no more unknowns are present in the approximation than in a standard finite element approximation. In this work, the intrinsic XFEM is employed for the simulation of incompressible two-fluid flows. Numerical results are shown for a number of test cases and prove the success of the method.

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Section: Description Of the Interfaces By The Level-set Methodsmentioning

confidence: 99%

The intrinsic XFEM for two‐fluid flows

Fries

2008

Numerical Methods in Fluids

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“…Lagrangian style front tracking schemes, e.g. Tryggvason et al [44,43] and marker particles [12,6,25,7,26,42], have also been used to model this class of problems. In addition, a popular alternative Eulerian front capturing scheme, the volume of fluid (VOF) method [14,24], is widely used.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Particle Level Set Method for Improved Interface Capturing

Enright

Fedkiw

Ferziger

et al. 2002

Journal of Computational Physics

919

699

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In this paper, we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field. Our method uses Lagrangian marker particles to rebuild the level set in regions which are under-resolved. This is often the case for flows undergoing stretching and tearing. The overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method. Our method compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution. The method is presented in three spatial dimensions.

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“…Naive central differencing of the lefthand side of equations 6 and 5 near the free surface can lead to O(∆x) errors in the pressure as noted by [14]. Later, [15] reduced the magnitude of these first order errors with the introduction of micro-cells.…”

Section: Pressure Boundary Treatmentmentioning

confidence: 99%

Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows

Enright

Nguyen

Gibou

et al. 2003

Volume 2: Symposia, Parts A, B, and C

114

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In this paper, we present an enhanced resolution capturing method for topologically complex two and three dimensional incompressible free surface flows. The method is based upon the level set method of Osher and Sethian to represent the interface combined with two recent advances in the treatment of the interface, a second order accurate discretization of the Dirichlet pressure boundary condition at the free surface (2002, J. Comput. Phys. 176, 205) and the use of massless marker particles to enhance the resolution of the interface through the use of the particle level set method (2002, J. Comput. Phys., 183, 83). Use of these methods allow for the accurate movement of the interface while at the same time preserving the mass of the the liquid, even on coarse computational grids. Also, these methods complement the level set method in its ability to handle changes in interface topology in a robust manner. Surface tension effects can be easily included in our method. The method is presented in three spatial dimensions, with numerical examples in both two and three spatial dimensions. Governing EquationsWe solve for inviscid, incompressible flow. The governing equations for momentum and mass conservation arewhere t is the time, u = (u, v, w) is the velocity field, p is the pressure, g = (0, g, 0) is gravity, ρ is the constant density of the liquid, and ∇ = (We use the free surface assumption so that the air has a constant pressure, p air , in space and time.The location of the liquid free surface is defined as the set of points where the level set function φ = 0, and the region occupied by the liquid is given by φ < 0. The level set equation [1],determines the evolution of the free surface in space and time. Geometrical information about the interface, e.g. normals and curvature, can be easily obtained from φ which we take as the signed distance to the interface. The unit outward normal is N = ∇φ/|∇φ| and the curvature is κ = ∇ · N. See [2] for more details.

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The Introduction of Micro Cells to Treat Pressure in Free Surface Fluid Flow Problems

Cited by 27 publications

References 15 publications

The intrinsic XFEM for two‐fluid flows

The intrinsic XFEM for two‐fluid flows

A Hybrid Particle Level Set Method for Improved Interface Capturing

Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows

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