THINC scaling method that bridges VOF and level set schemes

Kumar, Ronit; Cheng, Lidong; Xiong, Yunong; Xie, Bin; Abgrall, Rémi; Xiao, Feng

doi:10.1016/j.jcp.2021.110323

Cited by 23 publications

(16 citation statements)

References 56 publications

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“…The indicator function  is equal to unity when its coordinate resides in (x − 2) 2 + (y − 2.75) 2 ≤ 0.5 2 ∩ (|x − 2| ≥ 0.06 ∪ y > 2.85), or otherwise to zero, on a 4 × 4 square domain. The advection velocity field is 𝜋 (y − 2.0, 2.0 − x) and one revolution T = 2 is completed in exactly 2524 time steps, corresponding to maximum CFL THINC/QQ(local) 33 4.25 × −3 THINC/QQ(global) 38 2.45 × −3 THINC-scaling(GP=6) 35 1.58 × −3 THINC-scaling(GP=12) 35 1.27 × −3 15 for different types of grids with N = 200. It is seen that the present scheme outperforms other existing versions of THINC method (except the one that uses level-set function) in numerical accuracy on both structured grids and unstructured grids.…”

Section: D Solid Body Rotationmentioning

confidence: 99%

“…Another benchmark test was also carried out for 3D computation, which is used to evaluate the capability of a VOF scheme in resolving the distorted interface. 15,35,50,66 Initially, a sphere with a radius of 0.15 is centered on (0.5, 0.75, 0.5) and then stretched by a sheared velocity given by…”

Section: D Shear Flowmentioning

confidence: 99%

“…The maximum CFL number is set as 0.15 and the circle is transported for one revolution. First, we estimate the numerical errors and convergence orders with the two different options, (35) and (37), to compute the polynomial coefficients. We summarize all of the numerical errors and convergence rates in Tables 4-6 for quadrilateral, triangular, and polygonal grids with different resolutions.…”

Section: Numerical Reconstructions For the Interface Polynomialmentioning

confidence: 99%

“…This combination leads to a high‐quality THINC reconstruction function that accurately retrieves geometrical information from the level‐set field and ensures numerical conservation by using the VOF field, thus it brings substantial merits of the higher‐order polynomial for interface representation and enhances the capability to capture under‐resolved interface structure. More recently, THINC scaling scheme 35 has been proposed to completely unify the VOF and level‐set methods via the THINC reconstruction function, which largely eases the implementation of higher‐order interface reconstruction on unstructured grids. Besides, Kim et al 36 proposed a novel algebratic VOF scheme on the unstructured grids by blending the central difference and high‐resolution schemes, which shares the same spirit as THINC scheme to preserve the interface sharpness by using a logistic function.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Revisit to the THINC/QQ scheme: Recent progress to improve accuracy and robustness

Chen

Xie

Xiao

2022

Numerical Methods in Fluids

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In this article, we revisit to the THINC/QQ (tangent of hyperbola interface capturing method with quadratic surface representation and Gaussian quadrature) scheme to make thorough investigations on its numerical property. Furthermore, it presents some recent progress made extensively on THINC/QQ algorithm to improve numerical accuracy and robustness which include (1) construct the interface equation on the global coordinate so as to apply THINC/QQ on polygonal/polyhedral elements, which ensures the boundedness of numerical solutions as well; (2) determine the coefficients of reconstruction polynomial from the unit normal vector of interface to reduce computational cost and alleviate numerical diffusion; (3) represent the interface with a cubic polynomial rather than quadratic representation used in THINC/QQ to obtain better geometric fidelity; (4) provide an appropriate choice considering different combinations, such as the number of quadrature points and temporal discretization methods. The verification benchmark tests are carried out on different types of grids, which convinces that THINC/QQ scheme with normalization on global coordinate delivers higher accuracy and robustness than the original one, and demonstrates effective competition compared with other existing interface capturing methods.

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Section: D Solid Body Rotationmentioning

confidence: 99%

Section: D Shear Flowmentioning

confidence: 99%

Section: Numerical Reconstructions For the Interface Polynomialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Revisit to the THINC/QQ scheme: Recent progress to improve accuracy and robustness

Chen

Xie

Xiao

2022

Numerical Methods in Fluids

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“…For given velocity of a time-varying surface, there are extensive works in the literature on tracing and representing the surface approximately. We refer to [3,16,17,22,42] and the reference therein for level set methods, to [21,23,28] for volume-of-fluid methods, to [1,2,15] for momentof-fluid methods, and to [47,54] for front-tracking method. In a series of works [50][51][52][53], Zhang developed the cubic MARS algorithm for tracking the loci of free surface.…”

mentioning

confidence: 99%

High-order finite element methods for nonlinear convection-diffusion equation on time-varying domain

Zheng²

2021

Preprint

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A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semiimplicit in the sense that the boundary is traced explicitly with a high-order surface-tracking algorithm, while the convection-diffusion equation is solved implicitly with high-order backward differentiation formulas and fictitiousdomain finite element methods. By two numerical experiments for severely deforming domains, we show that optimal convergence orders are obtained in energy norm for third-order and fourth-order methods.

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A hybrid volume of fluid and level set interface capturing scheme with quartic surface representation for unstructured meshes

Xiong

Xiao

Xie

2022

Numerical Methods in Fluids

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In this article, we developed a hybrid volume of fluid (VOF) and level set interface capturing scheme with quartic surface representation for unstructured meshes. The so-called tangent of hyperbola interface capturing-scaling scheme with quartic surface representation (THINC-scaling/QSR) preserves the merits of the mass/volume conservativeness from the VOF scheme along with the geometric faithfulness from the level set scheme. Compared with linear/quadratic surface representation used in many other interface capturing schemes, the fluid interface is defined more precisely as a quartic polynomial surface of the THINC function which synchronize the interface between the VOF and level set functions in a straightforward solution procedure. We update the VOF function using a finite volume formulation. The level set function is first locally updated via a semi-Lagrangian method for interface cells and then reinitialized within each time step. Two-dimensional algorithm has been developed and verified by some benchmark tests on unstructured meshes. Convincing evidence suggests that the present scheme, with quartic surface representation, can provide high-fidelity solution with more pronounced sub-grid interface capturing capability than other most advanced methods.

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THINC scaling method that bridges VOF and level set schemes

Cited by 23 publications

References 56 publications

Revisit to the THINC/QQ scheme: Recent progress to improve accuracy and robustness

Revisit to the THINC/QQ scheme: Recent progress to improve accuracy and robustness

High-order finite element methods for nonlinear convection-diffusion equation on time-varying domain

A hybrid volume of fluid and level set interface capturing scheme with quartic surface representation for unstructured meshes

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