Spectral element solution of steady incompressible viscous free-surface flows

Ho, Lee-Wing; Rønquist, Einar M.

doi:10.1016/0168-874x(94)90065-5

Cited by 23 publications

(26 citation statements)

References 14 publications

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“…To simulate two-phase flow, an Arbitrary-Lagrangian-Eulerian (ALE) moving-mesh can be combined with hp-finite elements to obtain arbitrarily high orders of accuracy [15,22,23]. One simply increases the polynomial order of the approximation space (p) to increase the order of accuracy.…”

Section: Introductionmentioning

confidence: 99%

A hybrid level-set/moving-mesh interface tracking method

Perline

Helenbrook

2015

Applied Numerical Mathematics

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Section: Introductionmentioning

confidence: 99%

A hybrid level-set/moving-mesh interface tracking method

Perline

Helenbrook

2015

Applied Numerical Mathematics

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“…One approach to the treatment of surface tension is by variational techniques based on the Laplace-Beltrami operator on the free surface [33][34][35][36][37]. Another widely used approach is the continuum surface force (CSF) scheme [10,38].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

Croce

Griebel

Schweitzer

2009

Numerical Methods in Fluids

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SUMMARYIn this paper we present a three-dimensional Navier-Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties.Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region.We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and twodimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior.

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“…The spectral element formulation has been applied successfully to this flow (Ho and Rønquist [8]), wherein a fast convergence in space is achieved due to the inherent high-order spatial discretization (a characteristic of the spectral formulation).…”

Section: Introductionmentioning

confidence: 99%

The solution of viscous incompressible jet flows using non-staggered boundary fitted co-ordinate methods

Pacheco

2001

Int. J. Numer. Meth. Fluids

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Spectral element solution of steady incompressible viscous free-surface flows

Cited by 23 publications

References 14 publications

A hybrid level-set/moving-mesh interface tracking method

A hybrid level-set/moving-mesh interface tracking method

Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensions

The solution of viscous incompressible jet flows using non-staggered boundary fitted co-ordinate methods

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