Solving Immersed Interface Problems Using a New Interfacial Points-Based Finite Difference Approach

Mittal, H. V. R.; Ray, Rajendra K.

doi:10.1137/16m1106006

Cited by 11 publications

(11 citation statements)

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“…Numerical results show that the proposed methodology yields a good level of agreement with the reference data. It is noteworthy to mention that the immersed interface method employed in the present computations has already been validated for a fixed interface in three dimensions (Mittal and Ray, 2018). This opens up a possibility of their extension to address the problems of moving interfaces in three dimensions, which is the objective of our next paper.…”

Section: Discussionmentioning

confidence: 84%

“…Numerical solution of the pressure Poisson equation 26is challenging due to the discontinuities in the variables near the interface. To compute pressure, an efficient immersed interface scheme is enforced, according to Mittal and Ray (2018). The detailed discussion of this scheme is presented in Section 3.1.…”

Section: Numerical Methods Of Solutionmentioning

confidence: 99%

“…In order to discretize Eq. 26, the grid points in the computational domain are categorized into regular and irregular points (Mittal, 2016;Mittal et al, 2016;Mittal and Ray, 2018). A grid point is said to be an grid irregular point, if the finite difference stencil resulting from the approximation of the derivatives encloses points from both sides of Γ .…”

Section: Immersed Interface Treatmentmentioning

confidence: 99%

“…In the present paper, a coupling between LS and a recently developed higher order accurate immersed interface method (Mittal and Ray, 2018) has been proposed to address the problems of drops or bubbles evolving in incompressible, viscous flows due to surface tension force. The paramount feature of this immersed interface scheme is the use of Lagrange interpolation enclosing adjacent grid points and few special grid points named as "the interfacial points" as nodes.…”

mentioning

confidence: 99%

“…The use of this methodology in conjunction with the LS method allows us to deal with intricate interface geometries with a very simple mesh generation process. For a fixed interface, this methodology has been thoroughly validated in one, two, and three dimensions (Mittal and Ray, 2018). In the present work, this methodology is extended to solve moving interface problems governed by N-S equations for the first time.…”

mentioning

confidence: 99%

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A coupled immersed interface and level set method for simulation of interfacial flows steered by surface tension

Mittal

Ray

Gadêlha

et al. 2020

Exp. Comput. Multiph. Flow

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This work presents a methodology to address the problems of bubbles and drops evolving in incompressible, viscous flows due to the effect of surface tension. It is based on the combination of a recently developed immersed interface method to resolve discontinuities, with the level set (LS) method to reproduce the evolving interfaces. The paramount feature of this immersed interface method is the use of Lagrange interpolation enclosing grid points positioned in the vicinity of the interface and few exceptional grid points positioned on the interface. Different problems are considered to assert the accurateness of the proposed methodology, involving both simple and complex interface geometries. Precisely, the following problems are addressed: circular flow with a fixed interface, the dispersion of capillary waves, initially circular, ellipse, star shaped bubbles oscillating to an equilibrium state, and circular drops deforming in shear flows. The transient evolution of bubbles/drops in terms of their shapes, pressure profiles, velocity vectors, deformation ratios of major and minor axis is analyzed to observe the effect of surface tension. The proposed methodology is seen to recover the exact numerical equilibrium between the surface tension and pressure gradient in the vicinity of complex interface geometries as well, while recreating the flow physics with an adequate level of accuracy with well representation of overall trends. Moreover, the numerical results yield a good level of agreement with the reference data.

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Section: Discussionmentioning

confidence: 84%

Section: Numerical Methods Of Solutionmentioning

confidence: 99%

Section: Immersed Interface Treatmentmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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