A generic framework for design of interface capturing schemes for multi-fluid flows

Patel, Jitendra Kumar; Natarajan, Ganesh

doi:10.1016/j.compfluid.2014.10.005

Cited by 35 publications

(16 citation statements)

References 24 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first two test cases are the advection of the slotted circle in a rotational flow field introduced by Zalesak (1979) and the advection of a circle in a shear flow presented by Rudman (1997) which have simple exact solutions. These are frequently used in the multiphase community to check the performance of the advection schemes dealing with a non-uniform distribution of the Courant number and a considerable interface deformation, respectively (Ubbink and Issa, 1999;Zhang et al, 2014;Patel and Natarajan, 2015). For both, the accuracy of the simulation results is verified using the root mean square (RMS) error defined as…”

Section: Resultsmentioning

confidence: 99%

“…This paper presents this new idea that we call Modified Normalized Weighting Factor (MNWF) method which we apply for the numerical implementation of six blended HR schemes: CICSAM, MCICSAM-W, MCICSAM-Z, HRIC (Muzaferija et al, 1998), FBICS (Tsui et al, 2009), and CUIBS (Patel and Natarajan, 2015). The implementations are realized on the in-house finite-volume flow solver FASTEST, based on a block-structured collocated grid arrangement.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection schemes in the context of multiphase flows

Salguero

Schäfer

2020

Exp. Comput. Multiph. Flow

View full text Add to dashboard Cite

This work deals with a new methodology for the implementation of high-resolution (HR) schemes employed to advect the volume fraction in the volume of fluid (VOF) method, in which the numerical stability and convergence depend heavily on the numerical advection scheme and implementation method. The proposed method is based on the normalized weighting factor (NWF) method, which linearizes the normalized interpolation profile and rewrites the face value directly using the donor, acceptor, and upwind nodes. However, unlike the NWF, which is fully implicit and results in pentadiagonal linear systems, the new modified normalized weighting factor (MNWF) method only forms the implicit terms with the contribution of the donor and acceptor nodes, while the contribution of the upwind node explicitly forms part of the source term. Therefore, the method results in a tridiagonal linear system. The comparison of the new method with the deferred correction (DC), downwind weighting factor (DWF), and the RNWF methods shows that the MNWF requires about 5%–25% fewer iterations than DC and RNWF, and around 10%–85% less than DWF. Thus, a similar order of accuracy of the results can be o btained with less computational time.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection schemes in the context of multiphase flows

Salguero

Schäfer

2020

Exp. Comput. Multiph. Flow

View full text Add to dashboard Cite

show abstract

“…It must also be emphasized that the evaluation of the convective (

double-struckC double-struckO double-struckN double-struckV

) and diffusive (

double-struckD double-struckI double-struckF double-struckF

) fluxes is carried out in the same manner as in a collocated framework, which gives the methodology its nonstaggered flavor. The convective fluxes appearing in both the volume fraction advection and the normal momentum equation are obtained using the same high‐resolution bounded upwind‐biased scheme, whereas the diffusive fluxes are obtained using central differencing. We adopt an incremental fractional step approach wherein a Poisson equation is solved for the pressure correction

scriptP = p^{n + 1} - p^{n}

, and the face‐normal velocities are corrected algebraically to ensure a divergence‐free velocity field.…”

Section: Governing Equations and Numerical Methodologymentioning

confidence: 99%

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

Patel

Natarajan

2018

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

Summary We present a simple and cost‐effective curvature calculation approach for simulations of interfacial flows on structured and unstructured grids. The interface is defined using volume fractions, and the interface curvature is obtained as a function of the gradients of volume fractions. The gradient computation is based on a recently proposed gradient recovery method that mimicks the least squares approach without the need to solve a system of equations and is quite easy to implement on arbitrary polygonal meshes. The resulting interface curvature is used in a continuum surface force formulation within the framework of a well‐balanced finite‐volume algorithm to simulate multiphase flows dominated by surface tension. We show that the proposed curvature calculation is at least as accurate as some of the existing approaches on unstructured meshes while being straightforward to implement on any mesh topology. Numerical investigations also show that spurious currents in stationary problems that are dependent on the curvature calculation methodology are also acceptably low using the proposed approach. Studies on capillary waves and rising bubbles in viscous flows lend credence to the ability of the proposed method as an inexpensive, robust, and reasonably accurate approach for curvature calculation and numerical simulation of multiphase flows.

show abstract

“…The extension to VOF schemes, nicely summarized by Patel et al [43], requires a previous casting of the advection scheme into the same framework introduced in [42]. Plugging equation (46) into equation (45) .…”

Section: Energy-preserving Discretizationmentioning

confidence: 99%

An energy-preserving level set method for multiphase flows

Valle

Trias

González

2020

Journal of Computational Physics

View full text Add to dashboard Cite

The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the spirit of the wellknown symmetry-preserving and mimetic schemes, whose physics-compatible discretizations rely upon preserving the underlying mathematical structures of the space, we identify the corresponding structure and propose a new discretization strategy for curvature. The new scheme ensures conservation of mechanical energy (i.e., surface plus kinetic) up to temporal integration. Inviscid numerical simulations are performed to show the robustness of such a method.

show abstract

A generic framework for design of interface capturing schemes for multi-fluid flows

Cited by 35 publications

References 24 publications

A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection schemes in the context of multiphase flows

A Modified Normalized Weighting Factor method for improving the efficiency of the blended high-resolution advection schemes in the context of multiphase flows

A cost‐effective curvature calculation approach for interfacial flows on unstructured meshes

An energy-preserving level set method for multiphase flows

Contact Info

Product

Resources

About