An interface capturing method with a continuous function: The THINC method with multi-dimensional reconstruction

Satoshi,; Sugiyama, Kazuyasu; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro; Xiao, Feng

doi:10.1016/j.jcp.2011.11.038

Cited by 148 publications

(162 citation statements)

References 67 publications

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“…We employ the MTHINC method [12], in which a continuous sigmoid function (a hyperbolic tangent function) represents the interface in an algebraic form. The procedure enforces a grid-scale smoothness on the jump in the VOF profile across the interface, and avoids the numerical instability and diffusion.…”

Section: Methodsmentioning

confidence: 99%

“…Thus, in view of computational efficiency, the MTHINC method makes it easily possible to reduce a computational-load imbalance and a data communication in parallel computing. Further, reconsidering the algorithm in [12], we replaced "if" statements with mask processings for the procedure differed by the direction normal to the interface, improving the vector processing efficiency. To evaluate the unit normal vector n, we follow the Youngs approach [11], in which m in equation (1.8) is evaluated at the cell apex, and then it is interpolated onto the definition point of n. As in equation (1.4), φ rot (x, t) is determined from the initial (t = 0) distribution of φ rot in a semi-Lagrangian manner.…”

Section: Methodsmentioning

confidence: 99%

“…However, since the advection equation includes no diffusion term, a special treatment is required to prevent the numerical instability and to maintain the sharp interface, simultaneously. The numerical methods for maintaining the sharp interface include Simple Line Interface Calculation (SLIC) [10], Piecewise Linear Interface Calculation (PLIC) [11], and Multi-dimensional Tangent of Hyperbola INterface Capturing (MTHINC) [12] methods. We employ the MTHINC method, which imposes a grid-scale smoothness on the volume fraction profile across the interface, and relieves the singularity problem due to the jump thereof.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fixed-Mesh Approach for Gas-Liquid-Rigid Interaction Problems

Sugiyama

Okubo

Imahoko

et al. 2016

IOP Conf. Ser.: Earth Environ. Sci.

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Abstract.A fixed-mesh approach has been developed to facilitate predicting a certain class of gas-liquid-rigid interaction problems. All the basic equations are discretized on a Cartesian grid in a finite-difference manner. The Volume-Of-Fluid and Boundary Data Immersion methods are employed to treat the gas-liquid and fluid-rigid interfaces, respectively. A hybrid OpenMP-MPI approach is adopted for parallel computing. The developed code is validated through comparisons with experiments of an oil-air flow driven by a rotating disk with holes. The simulated results demonstrate the capability in capturing the velocity distributions. IntroductionGas-liquid flows driven by rotating rigid objects appear in many engineering applications. The interplay among centrifugal, buoyancy, viscous and surface tension forces gives rise to a rich behaviour involving the gas-liquid and fluid-rigid interface motions. Large-scale simulations of multiphase flows are expected to be useful for complementing experiments and gaining insight into the dynamics. It is desirable that the numerical method is efficient and robust for massively parallel computing.Direct numerical simulation of interfacial flows is often formidable mainly due to the spatiotemporal change in moving and deforming interface and the high degree of freedom. There are currently several approaches classified with respect to the numerical treatment how the kinematic and dynamic interactions are coupled on the interface. When addressing fluid engineering problems of practical applications with complex boundary, one has preferably employed a Lagrangian method using a finite element mesh. The numerical methods include Arbitrary Lagrangian Eulerian [1] and Deforming-Spatial-Domain/Stabilized Space-Time [2] approaches. If the body-fitted mesh is provided, the state-of-the-art Lagrangian approaches are satisfactory for achieving accurate predictions. However, for a system involving complex boundary, it requires considerable efforts to generate the high quality mesh and to reconstruct the mesh topology when the mesh element is added or deleted. Moreover, in parallel computing, one often encounters nontrivial issues how to keep the computational-load balance of each compute node in the domain decomposition, how to optimize the data communication between the Eulerian and Lagrangian frames, and so on. In the present study, we

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Fixed-Mesh Approach for Gas-Liquid-Rigid Interaction Problems

Sugiyama

Okubo

Imahoko

et al. 2016

IOP Conf. Ser.: Earth Environ. Sci.

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show abstract

“…A method that keeps the sharpness of the interface and also conserves the fluid mass usually needs a complex geometric reconstruction scheme; while a method that is based on the conventional discretization strategy for partial differential equations often leads to continuous smearing of the interface. A noticeable progress in the development of the volume-offluid method is the recent establishment of the THINC (tangent of hyperbola for interface capturing) scheme [12], in which a multi-dimensional hyperbolic tangent function instead of a step function is introduced to represent the interface within a cell where the volume-of-fluid function takes a value in between of 1 and 0. For a two-dimensional problem, the hyperbolic tangent function is written as [12]:…”

Section: A Volume-of-fluid Modelmentioning

confidence: 99%

“…It becomes well known that the successful model for such a study must include an algorithm that allows the complicated motion and deformation of the free surface to be accurately tracked or captured. The volume-of-fluid method, the level-set method, and their combinations have been proposed and then improved to meet such a need [10,44,17,12,29,36,35,37]. It has been reported that the numerical results obtained with these methods can catch the general features of a breaking wave but the details of the flow near the crest of the wave are not possible to be identified.…”

Section: Introductionmentioning

confidence: 99%

A coupled phase–field and volume-of-fluid method for accurate representation of limiting water wave deformation

Liu

2016

Journal of Computational Physics

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An efficient and accurate algebraic interface capturing method for unstructured grids in 2 and 3 dimensions: The THINC method with quadratic surface representation

Xie

Xiao

2014

Numerical Methods in Fluids

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SUMMARYWe present in this paper an efficient and accurate volume of fluid (VOF) type scheme to compute moving interfaces on unstructured grids with arbitrary quadrilateral mesh elements in 2D and hexahedral elements in 3D. Being an extension of the multi‐dimensional tangent of hyperbola interface capturing (THINC) reconstruction proposed by the authors in Cartesian grid, an algebraic VOF scheme is devised for arbitrary quadrilateral and hexahedral elements. The interface is cell‐wisely approximated by a quadratic surface, which substantially improves the numerical accuracy. The same as the other THINC type schemes, the present method does not require the explicit geometric representation of the interface when computing numerical fluxes and thus is very computationally efficient and straightforward in implementation. The proposed scheme has been verified by benchmark tests, which reveal that this scheme is able to produce high‐quality numerical solutions of moving interfaces in unstructured grids and thus a practical method for interfacial multi‐phase flow simulations. Copyright © 2014 John Wiley & Sons, Ltd.

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An interface capturing method with a continuous function: The THINC method with multi-dimensional reconstruction

Cited by 148 publications

References 67 publications

A Fixed-Mesh Approach for Gas-Liquid-Rigid Interaction Problems

A Fixed-Mesh Approach for Gas-Liquid-Rigid Interaction Problems

A coupled phase–field and volume-of-fluid method for accurate representation of limiting water wave deformation

An efficient and accurate algebraic interface capturing method for unstructured grids in 2 and 3 dimensions: The THINC method with quadratic surface representation

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