Compressive Interface Capturing Scheme For Arbitrary Meshes Research Articles

Performance analysis and reconstruction of interface capturing schemes for multiphase flows

This article aims to provide a roadmap for analysis of the interface capturing schemes and their possible modification with recommended design principles. Blending the suitable high resolution (HR) scheme with a bounded downwind (BD) scheme is the core of the development of any interface capturing scheme. However, the concrete guidelines for choice of HR and BD schemes are not clear. For this purpose, the HR and BD constituents of a popular scheme known as “Switching Technique for Advection and Capturing of Surfaces (STACS)” are analyzed. Subsequently, it is observed that the scheme fails to satisfy some critical design principles. This leads to a reconstruction of the scheme by introducing a newly compliant bounded downwind scheme. The novel re-constructed scheme is then accessed through typical advection problems, including the shear flow on structured and unstructured meshes. The scheme convincingly outperforms its parent scheme in all test cases irrespective of the Courant number. Moreover, it generates superior or at least at par results while compared with a few well-established schemes like Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) and Cubic Upwind Interpolation based Blending Scheme (CUIBS).

An efficient operator-split CICSAM scheme for three-dimensional multiphase-flow problems on Cartesian grids

Conventional algebraic Volume of Fluid (VOF) schemes utilize a Crank-Nicholson-based unsplit advection framework which is necessary for maintaining second-order accuracy in time as well as to allow extension to arbitrary meshes. However, the unsplit advection approach proves to be a bottleneck to computational performance for CFD solvers opting for non-body-conforming Cartesian grids for treating complex domains and immersed boundaries. To this effect, we propose a general operator-splitting framework for algebraic VOF schemes and develop a direction-split version of the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The resulting operator-split CICSAM (OS-CICSAM) scheme is compared against unsplit CICSAM as well as two recent algebraic VOF schemes for standard advection tests. In terms of volume tracking performance as well as interfacial shape preservation, it is demonstrated that OS-CICSAM attains comparable or lower L1 error norm, has rates of convergence intermediate to first and second order and is at least 600% faster in comparison to unsplit algebraic VOF schemes. The OS-CICSAM scheme is then coupled with the in-house CFD solver IITM-RANS3D. The robustness of the proposed scheme is established by applying to benchmark problems such as Rayleigh-Taylor instability and free surface wave interactions with a structure.

Effects of convective schemes and geometric reconstruction scheme on interface of multiple melt flows

Multi-phase polymer melt processing techniques, e.g., multi-layer co-extrusion and multi-melt multi-injection molding (M3IM), are typical methods for preparing multilayer composites. Numerical simulations are now broadly acknowledged to be an advanced and effective method to investigate the evolution of the interface between the melts during these processing techniques. However, how to describe the sharp interface between the melts precisely is still a big challenge. Herein, five different interpolation schemes were used to investigate the melt penetration in M3IM, paying close attention to the effects of different schemes on interface diffusion, wrinkle, and shape. In addition, the morphologies of the interface were characterized experimentally. By comparing the numerical results and experimental results, it can be concluded that the compressive interface capturing scheme for arbitrary meshes (CICSAM) is the most accurate method. Our work is instructive for expounding the variation patterns of interfacial morphologies during the multi-phase polymer melt processing.

Adjoint complement to the volume-of-fluid method for immiscible flows

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular challenge of the primal and the corresponding adjoint VoF-approach refers to the sharp interface treatment featuring discontinuous physical properties. Both the continuous adjoint two-phase system (integration-by-parts) and the corresponding dual compressive convection schemes (summation-by-parts) are derived for two prominent compressive convection schemes, namely the High Resolution Interface Capturing Scheme (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM). The dual scheme rigorously mirrors the primal Normalized-Variable-Diagram (NVD) stencils. Attention is restricted to steady state applications. Thus both the primal and the dual procedures are performed in pseudo-time and the backward integration of the dual approach is performed around the (pseudo-temporal) converged primal field. Therefore, the adjoint system experiences the same time step size restrictions as the primal system, is independent of the primal time horizon and forms a robust as well as an a priori stable adjoint solution process.The paper analyses the primal and adjoint equations for an engineering model problem. An analytical solution to the model problem is initially presented, which displays that the adjoint part does not offer a unique, non-trivial solution. As a remedy, an additional diffusive concentration term is introduced to the adjoint concentration equation. The imposed heuristic modification violates the dual consistency but strongly regularizes the solution of the adjoint system. The modification can be justified by reference to phase-separating diffuse-interface models and inheres a free mobility-parameter. Numerical results obtained from the modified approach are benchmarked against the analytical solution for the model problem. Supplementary, the influence of the modification on the sensitivities obtained from simulations for the two-dimensional flow around a submerged hydrofoil at Froude and Reynolds numbers of practical interest are discussed for a range of mobility-parameters. The final application refers to a shape-optimization of a generic 3D underwater vehicle and underlines a negligible influence of the free mobility parameter, even for an objective functional that directly depends on the manipulated (dual) field quantity.

An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

This paper presents an all-Mach method for two-phase inviscid flow in the presence of surface tension. A modified version of the Hartens–Lax–van Leer Contact (HLLC) solver is developed and combined for the first time with a widely used volume-of-fluid (VoF) method: the compressive interface capturing scheme for arbitrary meshes (CICSAM). This novel combination yields a scheme with both HLLC shock capturing as well as accurate liquid–gas interface tracking characteristics. It is achieved by reconstructing non-conservative (primitive) variables in a consistent manner to yield both robustness and accuracy. Liquid–gas interface curvature is computed via height functions and the convolution method. We emphasize the use of VoF in the interest of interface accuracy when modelling surface tension effects. The method is validated using a range of test-cases available in the literature. The results show flow features that are in sensible agreement with previous experimental and numerical work. In particular, the use of the HLLC-VoF combination leads to a sharp volume fraction and energy field with improved accuracy.

Unsteady 2D and 3D Navier-Stokes Solver with Application of Multigrid Scheme to Pressure Poisson Fractional Step on Arbitrary Unstructured Grids in Various Applications with Emphasis on Ship Motion

A 3D unsteady computer solver is presented to compute incompressible Navier-Stokes equations combined with the volume of fraction (VOF) method on an arbitrary unstructured domain. This is done to simulate fluid flows in various applications, especially around a marine vessel. The Navier-Stokes solver is based on the fractional steps method coupled with a finite volume scheme and collocated grids by which velocity components and pressure fields are defined at the center of the control volume. However, the fluxes are defined at the midpoint on their corresponding cell faces. On the other hand, the CICSAM (Compressive Interface Capturing Scheme for Arbitrary Meshes) scheme is applied to capture the free surface. In the presented fractional step method, the pressure Poisson equation suffers from poor convergence rate by simple iterative methods like Successive Overrelaxation (SOR), especially in simulating complex geometrics like a ship with appendages. Therefore, to accelerate the convergence rate, an agglomeration multigrid method is applied on arbitrary moving mesh for solving pressure Poisson equation with two well-known cycles, V and W. In order to maintain accuracy, the geometry details should not change in grid coarsening procedure. Therefore, the boundary faces are assumed to be fixed in all grids level. This assumption requires nonstandard cells in coarsening procedures. To investigate the performance of the applied algorithm, various flows including one and two-phase flows are studied in two and three dimensions. It is found that the multigrid method can speed up the convergence rate of fractional step twofold. In most cases (not all), W cycle displays better performance. It is also concluded that the efficiency of the cycle depends on the number of meshes and complexity of the problem and this is mainly due to the data transferring between grids. Therefore, the type of cycle should be selected judiciously and carefully, while considering the mesh size and flow properties.

Numerical study of advection schemes for interface-capturing using gradient smoothing method

Based on the newly developed gradient smoothing method (GSM), three interface-capturing schemes have been implementing using unstructured mesh. The volume of fluid (VOF) model is solved without explicitly interface reconstructing in the framework of GSM. The variables on upwind points are successfully approximated using centroid GSM (cGSM) scheme, which generally cannot be clearly defined on unstructured mesh. Compressive interface-capturing scheme for arbitrary meshes (CICSAM), flux-blending interface-capturing scheme (FBICS), and cubic upwind interpolation-based blending scheme (CUIBS) have been employed through three benchmark cases. The results indicate that FBICS and CUIBS can produce more accurate predictions using unstructured meshes.

A sharpness preserving scheme for interfacial flows

Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) [1] is a numerical scheme which is extensively used in commercial computational fluid dynamics solvers. However it generates significant numerical diffusion at higher Courant number. In order to improve its performance a modification is proposed in the existing algorithm to improve its interface capturing capability at high Courant number. The ULTIMATE QUICKEST scheme for interpolation of face value of volume fraction in the existing CICSAM algorithm is replaced by Fromm scheme [2] in the modified CISCAM algorithm. The Fromm scheme [2] imbibes better dispersion properties than conventional ULTIMATE QUICKEST. The modified algorithm is tested extensively for known two and three dimensional velocity fields. Also the scheme is coupled with Navier–Stokes’ solver and its performance is tested for collapse of water-column and bubble-rise with high surface tension coefficient. The modified scheme results in significant reduction of numerical diffusion and improves the interface capturing abilities.

Investigation of Different Droplet Formation Regimes in a T-junction Microchannel Using the VOF Technique in OpenFOAM

Here we aimed to investigate various droplet formation regimes in a two-dimensional T-junction microchannel geometry using the open source software OpenFOAM. Two incompressible fluids, continuous phase in the main channel and dispersed phase in the lateral channel, have been considered. The interFoam solver was used to simulate laminar flow with two incompressible and isothermal phases. We evaluated the capability of “Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM)” volume of fluid (VOF) technique of the OpenFOAM for modeling of the droplet formation and movement in different regimes. The flow behavior in the T-junction microchannel over a wide range of capillary numbers (0.006 to 0.12), volume flow rate ratio (0.125, 0.25, 0.5), and contact angle (130° to 180°) in the squeezing, dripping and jetting regimes were examined.The importance of parameters such as contact angle, capillary number, flow rate ratio, and Reynolds number at the time of separation, as well as the formation of droplets, was investigated in different regimes. We found that droplet detachment time increases by increasing the contact angle in the squeezing regime while increasing the contact angle in the dripping regime results in a decrease in the droplet detachment time. We compare the role of pressure gradient and shear stress forces in the droplet formation process in both dripping and squeezing regimes in details. We also provide a classification of two-phase flow regimes in the investigated T-junction microchannel in terms of three main parameters of, e.g., flow rate ratio, contact angle, and capillary number.

Numerical Simulation on Interface Evolution and Impact of Flooding Flow

A numerical model based on Navier-Stokes equation is developed to simulate the interface evolution of flooding flows. The two-dimensional fluid domain is discretised by structured rectangular elements according to finite volume method (FVM). The interface between air and liquid is captured through compressive interface capturing scheme for arbitrary meshes (CICSAM) based on the idea of volume of fluid (VOF). semiimplicit method for pressure linked equations (SIMPLE) scheme is used for the pressure-velocity coupling. A second order upwind discretization scheme is applied for the momentum equations. Both laminar flow model and turbulent flow model have been studied and the results have been compared. Previous experiments and other numerical solutions are employed to verify the present results on a single flooding liquid body. Then the simulation is extended to two colliding flooding liquid bodies. The impacting force of the flooding flow on an obstacle has been also analyzed. The present results show a favourable agreement with those by previous simulations and experiments.

Numerical investigation of wave attenuation by vegetation using a 3D RANS model

Vegetation has been recognized as an important natural shoreline protection against storm surges and waves. Understanding of wave–vegetation interaction is essential for assessing the ability of vegetation patches, such as wetlands, to mitigate storm damages. In this study the wave attenuation by vegetation is investigated numerically using a 3-D model which solves the Reynolds-Averaged Navier–Stokes equations (RANS) by means of a finite-volume method based on collocated hexahedron mesh. A mixing length model is used for turbulence closure of the RANS equations. The water surface boundary is tracked using the Volume-of-Fluid (VOF) method with the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) to solve the VOF advection equation. The presence of vegetation is taken into account by adding the vegetation drag and inertia forces to the momentum equations. The model is validated by several laboratory experiments of short wave propagation through vegetation over flat and sloping beds. The comparisons show good agreement between the measured data and calculated results, but the swaying motion of flexible vegetation which is neglected in this study can influence the accuracy of the wave height predictions. The model is then applied to one of the validation tests with different vegetation properties, revealing that the wave height attenuation by vegetation depends not only on the wave conditions, but also the vegetation characteristics such as vegetation height and density.

A refined volume-of-fluid algorithm for capturing sharp fluid interfaces on arbitrary meshes

This paper presents a new volume-of-fluid scheme (M-CICSAM), capable of capturing abrupt interfaces on meshes of arbitrary topology, which is a modification to the compressive interface capturing scheme for arbitrary meshes (CICSAM) proposed in the recent literature. Without resort to any explicit interface reconstruction, M-CICSAM is able to precisely model the complex free surface deformation, such as interface rupture and coalescence. By theoretical analysis, it is shown that the modified CICSAM overcomes three inherent drawbacks of the original CICSAM, concerning the basic differencing schemes, the switching strategy between the compressive downwind and diffusive high-resolution schemes, and the far-upwind reconstruction technique on arbitrary unstructured meshes. To evaluate the performance of the newly proposed scheme, several classic interface capturing methods developed in the past decades are compared with M-CICSAM in four test problems. The numerical results clearly demonstrate that M-CICSAM produces more accurate predictions on arbitrary meshes, especially at high Courant numbers, by reducing the numerical diffusion and preserving the interface shape.

3-D finite-volume model of dam-break flow over uneven beds based on VOF method

A 3-D numerical model has been developed to simulate dam-break flow over uneven beds in irregular domains. The model solves the Reynolds-Averaged Navier–Stokes equations (RANS) using a finite-volume method based on collocated mesh that fits the solid boundaries such as bed and walls. The velocity and pressure coupling is achieved using the PISO algorithm and the Rhie and Chow’s momentum interpolation. The Smagorinsky eddy viscosity model is used for turbulence closure of the RANS equations. The movement of water surface is captured using the Volume-of-Fluid (VOF) method with the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) to solve the VOF advection equation. The accuracy and robustness of the model has been tested using several small- and large-scale laboratory experiments of dam-break flow. Some comparisons between the calculated results by the present model and those calculated by depth-averaged 2-D and 3-D models in the literature are presented.

An evaluation of interface capturing methods in a VOF based model for multiphase flow of a non-Newtonian ceramic in tape casting

The aim of the present study is to evaluate the different interface capturing methods as well as to find the best approach for flow modeling of the ceramic slurry in the tape casting process. The conventional volume of fluid (VOF) method with three different interpolation methods for interface capturing, i.e. the Geometric Reconstruction Scheme (GRS), High Resolution Interface Capturing (HRIC) and Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM), are investigated for the advection of the VOF, both for Newtonian and non-Newtonian cases. The main purpose is to find the best method for the free surface capturing during the flow of a ceramic slurry described by a constitutive power law equation in the tape casting process. First the developed model is tested against well-documented and relevant solutions from literature involving free surface tracking and subsequently it is used to investigate the flow of a La0.85Sr0.15MnO3 (LSM) ceramic slurry modeled with the Ostwald de Waele power law. Results of the modeling are compared with corresponding experimental data and good agreement is found.

Numerical Simulation of 3D Free-Surface Flows by Using CIP-based and FV-based Methods

In this paper, three-dimensional free-surface flows are simulated by using two different numerical methods, the constrained interpolation profile (CIP)-based and finite volume (FV)-based methods. In the CIP-based method, the governing equations are solved on stationary staggered Cartesian grids by a finite difference method, and an immersed boundary technique is applied to deal with wave-body interactions. In the FV-based method, the governing equations are solved by applying collocated finite volume discretization, and body-fitted meshes are used. A free-surface boundary is considered as the interface of the multi-phase flow with air and water, and a volumeof-fluid (VOF) approach is applied to trace the free surface. Among many variations of the VOF-type method, the tangent of hyperbola for interface capturing (THINC) and the compressive interface capturing scheme for arbitrary meshes (CICSAM) techniques are used in the CIP-based method and FV-based method, respectively. Numerical simulations have been carried out for dam-breaking and wave-body interaction problems. The computational results of the two methods are compared with experimental data and their differences are observed.

Modeling the disintegration of modulated liquid jets using volume-of-fluid (VOF) methodology

In this study, we present the numerical investigations on the effect of finite velocity modulations imposed on an otherwise unperturbed cylindrical liquid jet issuing into stagnant gas. Sinusoidal velocity fluctuations of finite frequency and amplitude are imposed at the liquid jet inlet and the resulting liquid jet surface deformation is captured using a volume of fluid (VOF) methodology, utilizing compressive interface capturing scheme for arbitrary meshes (CICSAM) scheme. Variation of the simulation parameters, comprising of the mean liquid jet velocity, modulation amplitude and frequency grouped together using a set of non-dimensional parameters, leads to the formation of a wide gamut of reproducible liquid structures such as waves, upstream/downstream directed bells, chains of droplets similar to those observed in experiments. Elaborate tests on the effect of injection velocity and inlet jet diameter are investigated to characterize the breakup process. The computations efficiently capture the diverse flow structures generated by the evolving modulated liquid jet inclusive of several non-linear dynamics such as growth of surface waves, ligament interaction with shear vortices and its subsequent thinning process. The simulations identify the deterministic behavior of modulated liquid jets to predict liquid disintegration modes under given set of non-dimensional parameters.

Volume of fluid methods for immiscible-fluid and free-surface flows

This article reviews and analyzes a number of numerical methods to track interfaces in multiphase flows. Several interface tracking methods can be found in literature: the level-set method, the marker particle method, the front tracking method and the volume of fluid method (VOF) to name a few. The volume of fluid method has an advantage of being conceptually simple, reasonably accurate and phenomena such as interface breakup and coalescence are inherently included. Over the years a number of different techniques to implement the VOF method have been devised. This article gives a basic introduction to the VOF method and focuses on four VOF methods: flux-corrected transport (FCT) by Boris et al. [J.P. Boris, D.L. Book, Flux-corrected transport. I: SHASTA, a fluid transport algorithm that works, J. Comput. Phys. 11 (1973) 38-69], Lagrangian piecewise linear interface construction (L-PLIC) by van Wachem and Schouten [B.G.M. van Wachem, J.C. Schouten, Experimental validation of 3-d Lagrangian VOF model: bubble shape and rise velocity, AIChE 48 (12) (2002) 2744-2753], Compressive interface capturing scheme for arbitrary meshes (CICSAM) by Ubbink [O. Ubbink, Numerical prediction of two fluid systems with sharp interfaces, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, 1997] and inter-gamma scheme by Jasak and Weller [H. Jasak, H.G. Weller, Interface-tracking capabilities of the InterGamma differencing scheme, Technical Report, Imperial College, University of London, 1995]. A detailed description of these schemes is given and implemented into an in-house fully coupled solver. Further, the performance of these schemes is examined employing a number of tests to analyze their strengths and weaknesses. Their advantages and limitations are discussed. (C) 2008 Elsevier B.V. All rights reserved.

Mathematical Modeling of Incompressible MHD Flows with Free Surface

Mathematical model for incompressible magnetohydrodynamics (MHD) flows with complex free surfaces has been developed, the transient 3D Navier–Stokes equations with Lorentz force induced by static magnetic field are solved. In this model, the simplified marker and cell (SMAC) method is used for solving the Navier–Stokes equations, the dynamic conditions at free surface are implemented through the continuum surface force (CSF) model with the volume of fluid (VOF) method, the compressive interface capturing scheme for arbitrary meshes (CICSAM) scheme is used for the VOF convection, and anti-diffusion procedure is conducted to suppress the numerical diffusion caused by the VOF convection. Effect of the anti-diffusion operation is investigated, and coalescence of two gas bubbles and impact of a drop on shallow liquid film are examined in order to verify the validity of the present mathematical model. As MHD flow examples, pouring of liquid metal into a rectangle insulated container and coalescence of two gas bubbles in the static magnetic field are simulated.

Three‐dimensional numerical simulation of injection mold filling with a finite‐volume method and parallel computing

AbstractThis paper presents a finite‐volume approach with a hybrid flexible distributed/shared memory parallel programming model to simulate the injection mold filling process. The simulation program deals with a three‐dimensional nonisothermal, non‐Newtonian flow with moving interfaces. The finite‐volume method is implemented to solve the governing equations, while a compressive interface capturing scheme for arbitrary meshes (CICSAM) is used to track the advancing melt fronts. For parallel computing, the program implements the “greedy algorithm'' as the domain decomposition method to distribute the computational work equally among the different computational nodes, and the message passing interface is used to communicate and exchange information between the computational nodes. For the symmetric multiprocessing nodes, OpenMP directives are integrated in the application's loop constructions. This approach effectively improved the solution efficiency in terms of computational time and accuracy. Three‐dimensional mold filling examples, which were used to verify and validate the numerical implementation and to demonstrate its performance and capabilities, are presented. © 2007 Wiley Periodicals, Inc. Adv Polym Techn 25:247–258, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/adv.20076

Three-dimensional numerical simulation of viscoelastic flow through an abrupt contraction geometry

AbstractA numerical scheme for simulating three-dimensional viscoelastic flow was developed. The three-dimensional finite volume method (FVM) based on a non-staggered grid and the semi-implicit method for pressure-linked equations (SIMPLE) were adopted to solve the continuity and momentum equations. As we used a non-staggered grid, the momentum interpolation method (MIM) was employed to avoid checkerboard type pressure fields. Viscoelastic properties of the fluid were described by the Phan-Thien and Tanner (PTT) model, which was treated by the compressive interface capturing scheme for arbitrary meshes (CICSAM). The elastic viscous split stress scheme (EVSS) was used to decouple the velocity and the stress fields. Algebraic equations obtained by the above schemes were handled by an iterative solver and a multi-grid method was applied to accelerate convergence. In order to verify the scheme developed in this study, Newtonian flow in a rectangular duct was studied and the resulting velocity fields were compared with the analytical flow fields. Then viscoelastic flow in 4:1 contraction geometry, one of the most frequently used benchmarking problems, was predicted by applying the fully three-dimensional finite volume method.