Parabolic interface reconstruction for 2D volume of fluid methods

Remmerswaal, Ronald A.; Veldman, Arthur

doi:10.1016/j.jcp.2022.111473

Cited by 13 publications

(11 citation statements)

References 34 publications

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“…The accuracy of the distance function is essential for convergence: we found that using a PLIC reconstruction resulted in an insufficiently accurate distance function which resulted in a lack of convergence for R ρ = 10 −3 . The results obtained here use a piecewise parabolic reconstruction of the interface (the PLVIRA method from Remmerswaal and Veldman [27] was used).…”

Section: Validationmentioning

confidence: 99%

A sharp, structure preserving two-velocity model for two-phase flow

Remmerswaal¹,

Veldman²

2022

Preprint

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The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the two-velocity model of the two-phase Navier-Stokes equations. This results in the ability to model the shear layer, rather than resolving it, by allowing for a velocity discontinuity in the direction(s) tangential to the interface.In a previous paper (Remmerswaal and Veldman (2022), arXiv:2209.14934) we have discussed the transport of mass and momentum, where the two fluids were not yet coupled. In this paper an implicit coupling of the two fluids is proposed, which imposes continuity of the velocity field in the interface normal direction. The coupling is included in the pressure Poisson problem, and is discretised using a multidimensional generalisation of the ghost fluid method. Furthermore, a discretisation of the diffusive forces is proposed, which leads to recovering the continuous one-velocity solution as the interface shear layer is resolved.The proposed two-velocity formulation is validated and compared to our one-velocity formulation, where we consider a multitude of two-phase flow problems. It is demonstrated that the proposed two-velocity model is able to consistently, and sharply, approximate solutions to the inviscid Euler equations, where velocity discontinuities appear analytically as well. Furthermore, the proposed two-velocity model is shown to accurately model the interface shear layer in viscous problems, and it is successfully applied to the simulation of breaking waves where the model was used to sharply capture free surface instabilities.

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Section: Validationmentioning

confidence: 99%

A sharp, structure preserving two-velocity model for two-phase flow

Remmerswaal¹,

Veldman²

2022

Preprint

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“…For the MOF method it is known that not all reference moments result in stability w.r.t. perturbations of the reference first moment [45], just as there are reference moments which result in multiple solutions 1 to the optimisation eq. (3.64).…”

Section: The Moment Of Fluid Reconstruction Algorithmmentioning

confidence: 99%

“…Illustration of steps 1.1 and 1.2 for the first dimensionally unsplit centroid advection step of the WYA method. The red dashed rectangles correspond to the DRs, whereas the green dashed-dotted line is part of the boundary of both staggered control volumes ω f 1 , ω f 2 , where F [1] (c) = {f1, f2}.…”

Section: Unsplit Donating Regionsmentioning

confidence: 99%

“…, where H [1] , H [2] denote the first and second derivative of H, respectively. The averaged LHF, which was defined in eq.…”

Section: Curvature Computation Using a Local Height-functionmentioning

confidence: 99%

“…the containment system) as well as in the frame of reference of the phase interface. It is the latter1 Some of the results from section 6.5, which favour the use of the LW flux interpolant, were not yet available when performing (most of) the simulations in this chapter. The Fromm flux interpolant is used in this chapter with α † = 0.5, which is convergent under mesh refinement, but in future work we would advocate the use of the LW flux interpolant.…”

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confidence: 99%

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Numerical Modelling of Variability in Liquid Impacts

Remmerswaal¹

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Piecewise circular interface construction using height functions

Maity,

Sundararajan,

Velusamy

2024

Numerical Methods in Fluids

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A piecewise circular interface construction (PCIC) method is described, where height functions based curvature estimates are directly utilised for accurate interface reconstruction under the framework of volume of fluid method. The present work is an attempt to develop a robust and accurate higher order interface reconstruction algorithm that is capable of accurate simulation of surface tension dominated flows. The proposed hybrid method (H‐PCIC) is thus able to take advantage of merits of both PCIC and HF methods, achieving at least second order convergence with respect to both interface reconstruction and curvature computation. This is in addition to the significantly superior quality of the reconstructed interface with respect to PLIC methods. This seamless blending of the HF and PCIC quantities is enabled by c0‐correction procedures applied to base PLIC and initial PCIC steps. More recent variants of the height function method with variable stencil size are used for calculation of radius of curvature. The capability of this proposed method towards simulation of flow problems within a well‐balanced two‐phase solver is established with help of multiple complex two‐phase flow problems. This validation exercise also demonstrates the capability of PCIC class of methods towards solutions of two‐phase flows with intricate physics.

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Parabolic interface reconstruction for 2D volume of fluid methods

Cited by 13 publications

References 34 publications

A sharp, structure preserving two-velocity model for two-phase flow

A sharp, structure preserving two-velocity model for two-phase flow

Numerical Modelling of Variability in Liquid Impacts

Piecewise circular interface construction using height functions

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