Discussion on Momentum Interpolation Method for Collocated Grids of Incompressible Flow

Yu, Bo; Tao, Wen‐Quan; Wei, Jinjia; Kawaguchi, Yasuo; Tagawa, Tetsuya; Ozoe, Hiroyuki

doi:10.1080/10407790190053879

Cited by 79 publications

(62 citation statements)

References 22 publications

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“…Another undesirable feature of the original Rhie-Chow interpolation is that the converged steady state cell-face mass flux calculated using Eq. (19) depends on the time step size [30,32,33]. This issue has manifested itself in our study through the consistency violation of the numerical method for small time steps.…”

Section: Discretisation Of the Mathematical Modelmentioning

confidence: 98%

“…It is well known that the original Rhie-Chow interpolation could fail to prevent a checkerboard pressure field if a very small time step is used [29,[31][32][33]. Explanation for such behaviour can be provided by analysing limiting values of expressions (20) when time step size tends to zero:…”

Section: Discretisation Of the Mathematical Modelmentioning

confidence: 99%

“…This issue has manifested itself in our study through the consistency violation of the numerical method for small time steps. We have eliminated both of these two deficiencies by using the modified interpolation proposed by Yu et al [33] for a fixed mesh. Hence, in our modified Rhie-Chow (mRC) interpolation, terms (H/a) f and (1/a) f in Eqs.…”

Section: Discretisation Of the Mathematical Modelmentioning

confidence: 99%

“…Here we came across a limitation of the original Rhie and Chow interpolation connected with the application of very small time steps (due to semi-implicit treatment of surface tension forces). It is known that the original Rhie and Chow interpolation is time step size dependent and that it could fail to prevent the appearance of a checkerboard pressure field if a very small time step size is used [29][30][31][32][33]. Yu et al [33] proposed a remedy for this problem on a fixed mesh and we have extended their solution, obtaining time step size independent Rhie and Chow interpolation on a moving mesh.…”

Section: Introductionmentioning

confidence: 99%

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A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

2012

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a b s t r a c tThis paper describes a moving mesh interface tracking method implemented in OpenFOAM for simulating three-dimensional (3-D) incompressible and immiscible two-phase interfacial fluid flows with dominant surface tension forces. Collocated finite volume (FV) method is used for spatial discretisation of Navier-Stokes equations on moving polyhedral mesh. The mesh consists of two parts separated on interface. Fluid flow is solved on each mesh separately and coupling is accomplished in an iterative manner by enforcing the kinematic and dynamic condition at the interface. Surface tension force is calculated on arbitrary polygonal surface mesh with second order accuracy using a ''force-conservative'' approach. Arbitrary polyhedral mesh adapts to the time-varying shape of the interface using vertex-based automatic mesh motion solver which calculates the motion of internal points based on the prescribed motion of interface points by solving the variable diffusivity Laplace equation discretised using the finite element method. The overall solution procedure based on iterative PISO algorithm with modified Rhie-Chow interpolation is second-order accurate in space and time, as is confirmed by numerical experiments on small amplitude sloshing in a two-dimensional (2-D) tank, 3-D droplet oscillation and buoyant rise of a 3-D air bubble in water. Numerical results are found to be in excellent agreement with available theoretical and experimental results.

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Section: Discretisation Of the Mathematical Modelmentioning

confidence: 98%

Section: Discretisation Of the Mathematical Modelmentioning

confidence: 99%

Section: Discretisation Of the Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

2012

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“…where the value ofÛ Û U j is obtained using the Momentum Interpolation Method (MIM) [7], as it will be explained later.…”

Section: Governing Equations and Numerical Discretizationmentioning

confidence: 99%

A higher-order finite volume method with collocated grid arrangement for incompressible flows

Ramírez¹,

Nogueira²,

Khelladi³

et al. 2015

Computational Methods and Experimental Measurements XVII

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A high accurate finite volume method based on the use of Moving Least Squares (MLS) approximants is presented for the resolution of the incompressible Navier-Stokes equations on unstructured grids. Moreover, in order to eliminate the decoupling between pressure and velocity, we present a new Momentum Interpolation Method that allows interpolations better than linear on any kind of mesh. The accuracy of the new method is evaluated by a steady and unsteady test cases.

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2011

Computational Thermo‐Fluid Dynamics

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Discussion on Momentum Interpolation Method for Collocated Grids of Incompressible Flow

Cited by 79 publications

References 22 publications

A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow

A higher-order finite volume method with collocated grid arrangement for incompressible flows

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