 |
 |
 |
|
|
|
[Sponsors] | ||||
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Joachim Balis, Frederik Jacobs, Georg May
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Joseph O’Connor, Sylvain Laizet, Andrew Wynn, Wouter Edeling, Peter V. Coveney
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Brian C. Vermeire
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Constantin Zenz, Michele Buttazzoni, Tobias Florian, Katherine Elizabeth Crespo Armijos, Rodrigo Gómez Vázquez, Gerhard Liedl, Andreas Otto
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Björn Sjögreen, H.C. Yee
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): A.P.S. Wheeler
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Jin Bao, Zhaoli Guo
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Lucka Barbeau, Shahab Golshan, Jieyao Deng, Stéphane Étienne, Cédric Béguin, Bruno Blais
Publication date: 15 January 2024
Source: Computers & Fluids, Volume 268
Author(s): Alexis Giauque, Corentin Giguet, Aurélien Vadrot, Christophe Corre
Publication date: Available online 17 November 2023
Source: Computers & Fluids
Author(s): Joel A. McQuaid, Christoph Brehm
We developed a novel computational framework that consists of a fully parallelized solution method using algebraic splitting and semi-implicit scheme for monolithic FSI equation systems, the parallel CG method, and a pixel model wing combined with explicit node-positioning. Using the proposed framework, we found that feathering and cambering motions in flapping insect wings will be given based on the equilibrium between wing's elastic and aerodynamic forces, and these motions are enhanced by the wing's inertial force.
In flapping insect wings, veins support flexible wing membranes such that the wings form feathering and cambering motions passively from large elastic deformations. These motions are essentially important in unsteady aerodynamics of insect flapping flight. Hence, the underlying mechanism of this phenomenon is an important issue in studies on insect flight. Systematic parametric studies on strong coupling between a model wing describing these elastic deformations and the surrounding fluid, which is a direct formulation of this phenomenon, will be effective for solving this issue. The purpose of this study is to develop a robust numerical framework for these systematic parametric studies. The proposed framework consists of two novel numerical methods: (1) A fully parallelized solution method using both algebraic splitting and semi-implicit scheme for monolithic fluid–structure interaction (FSI) equation systems, which is numerically stable for a wide range of properties such as solid-to-fluid mass ratios and large body motions, and large elastic deformations. (2) A structural mechanics model for insect flapping wings using pixel modeling (pixel model wing), which is combined with explicit node-positioning to reduce computational costs significantly in controlling fluid meshes. The validity of the proposed framework is demonstrated for some benchmark problems and a dynamically scaled model incorporating actual insect data. Finally, from a parametric study for the pixel model wing flapped in fluid with a wide range of solid-to-fluid mass ratios, we find a FSI mechanism of feathering and cambering motions in flapping insect wings.
A hydrostatic multilayered SWE system with spatiotemporally varying layer ratios is proposed in the current study. Periodical variation of layer ratios compounded with the spatial variability of the same. The existence of layer bounds as limits of integration only or a vertical conforming grid.
The study of multilayered shallow water equations has developed from a consideration of immiscible layers as a vertical mesh to the layer bounds as imaginary extremes for vertical integration of the flow equations. In the current work, a quasi three-dimensional flow model has been developed with the consideration of the spatiotemporal flexibility/variability of the pervious vertical discretization/layer ratios. Thus, in principle, vertical layering offers a nonuniform grid with a temporal variation. The system of equations thus formulated comprises a conservative part and the appended source/sink terms. These source/sink terms pertain to the inter-layer interactions such as mass/momenta transfer and interfacial stress, which have been treated in a novel implicit form alongwith the subgrid-scale eddy-viscosity for interlayer shear. They are integrated into the system through different physical considerations so as to arrive at a well-balanced numerical scheme in a regular finite volume grid. The model has been validated through the standard test-cases highlighting the conservation properties and the model's adaptability to uniform and nonuniform vertical meshes alongwith the spatiotemporal transitions of layer ratios, with a specific interest in limiting cases of wet/dry fronts. The increase in layer ratios tends to nearly replicate the full-scale model results in experimental scenarios at a lesser computational overhead.
Flow resistance co-efficient of meandering river in alluvial plain and its prediction using artificial neural network.
A proper estimation of flow resistance coefficient of river is essential for precise simulations of river hydraulics. In addition to the cross-sectional geometry and hydraulic parameters, the alignment of the channel affects the flow resistance coefficient in case of meandering rivers. In the present study, a rigorous field study of 131 km along the Barak River was conducted to assess the influence of meandering on the flow resistance coefficient. The values of flow resistance co-efficient were calculated using Chezy and Manning's equations with measured field data and the values from both are compared. However, the variation in the flow resistance co-efficient along the channel calculated from Manning's equation is significantly less as it does not consider the undulation and meandering. Using these field data, an artificial neural network (ANN) model has been developed to predict the cross-sectional averaged flow resistance for meandering river. The model considered the influence of relative curvature, depth of flow, bed particle size, Froude number and Reynolds number including water temperature for accurate predictions of flow resistance coefficient. The ANN model was tested and validated using 237 field data sample. The values of the statistical parameters indicate a very good fit to the training dataset with coefficient of determination (R 2) = 0.9566 for training and good fit for testing with R 2 = 0.8131. The developed ANN model has been compared with other model with the same data set to check its applicability.
We propose two enhanced approaches of physics informed neural networks (PINN) for solving the challenging Navier–Stokes equation (NSE). The first approach improves the model by approximating the velocity components and integrating a pressure-based loss function. The second approach directly approximates the NSE solution without assumptions, significantly reducing training duration while maintaining high accuracy. We successfully apply this approach to solve the three-dimensional NSE, demonstrating the advantages of our models in terms of trainability, flexibility, and efficiency.
Fluid mechanics is a critical field in both engineering and science. Understanding the behavior of fluids requires solving the Navier–Stokes equation (NSE). However, the NSE is a complex partial differential equation that can be challenging to solve, and classical numerical methods can be computationally expensive. In this paper, we propose enhancing physics-informed neural networks (PINNs) by modifying the residual loss functions and incorporating new computational deep learning techniques. We present two enhanced models for solving the NSE. The first model involves developing the classical PINN for solving the NSE, based on a stream function approach to the velocity components. We have added the pressure training loss function to this model and integrated the new computational training techniques. Furthermore, we propose a second, more flexible model that directly approximates the solution of the NSE without making any assumptions. This model significantly reduces the training duration while maintaining high accuracy. Moreover, we have successfully applied this model to solve the three-dimensional NSE. The results demonstrate the effectiveness of our approaches, offering several advantages, including high trainability, flexibility, and efficiency.
Fast and highly accurate numerical solutions for transport and dispersion of phosphogypsum in the coastal zone of Jorf Lasfar on the Atlantic Ocean at Morocco can be achieved by using a multilevel adaptive semi-Lagrangian finite element method. A class of enrichment techniques has been used to discretize the governing equations and the obtained results are assessed for different release scenarios.
We present a numerical method for modelling and simulation of transport and dispersion of phosphogypsum in the Jorf Lasfar coastal zone located on the Atlantic Ocean at Morocco. The governing equations consist of the well-established barotropic ocean model including the barometric pressure, friction terms, Coriolis and wind stresses. To model transport and dispersion of phosphogypsum we consider an advection-diffusion equation with an anisotropic dispersion tensor and source terms. As a numerical solver, we propose a novel multilevel adaptive semi-Lagrangian finite element method. The proposed method combines the modified method of characteristics to deal with convection terms, the finite element discretization to handle complex geometries, a projection-based algorithm to solve the Stokes problem, and an adaptive L2$$ {\mathrm{L}}^2 $$-projection using quadrature rules to improve the efficiency and accuracy of the method. Numerical results are presented to demonstrate the high resolution of the proposed method and to confirm its capability to provide accurate and efficient simulations for transport and dispersion of phosphogypsum in the Jorf Lasfar coastal zone.
Application of a nonuniform mesh IBM can significantly reduce the mesh requirement for particle-laden turbulent channel flow simulation while being capable of better resolving the near-wall small-scale flow dynamics. Nonuniform mesh simulations, while with a reduction of the CPU time by a factor of more than 7, are shown to provide comparable results as those based on a uniform mesh. The effects of finite-size solid particles on the mean flow velocity, Reynolds stress, and root-mean-squared velocity fluctuations are presented, to demonstrate various aspects of turbulence modulation by solid particles.
Particle-resolved simulations of turbulent particle-laden flows provide a powerful research tool to explore detailed flow physics at all scales. However, efficient particle-resolved simulations for wall-bounded turbulent particle-laden flows remain a challenging task. In this article, we develop a simulation approach for a turbulent channel flow laden with finite-size particles on a nonuniform mesh by combining the discrete unified gas kinetic scheme (DUGKS) and the immersed boundary method (IBM). The standard discrete delta function was modified according to reproducible kernel particle method to take into account mesh non-uniformity and correctly conserve force moments. Simulation results based on uniform and nonuniform meshes are compared to validate and examine the accuracy of the nonuniform mesh DUGKS-IBM. Finally, the computational performance of the nonuniform mesh DUGKS-IBM is discussed.
Complement is given to the physics-based interpretation of a Robin-type wall closure and then the slip-wall model is improved by redefining the slip length. The improved wall model is implemented in the local domain-free discretization method for large eddy simulation of high-Re turbulent flows. The predicted results agree well with the referenced experimental data and numerical results.
In this paper, a slip-wall model for large eddy simulation (LES) is improved and implemented in an immersed boundary method named the local domain-free discretization (DFD) method. Considering that the matching location may be in the viscous sublayer, the physics-based interpretation of a Robin-type wall closure is complemented. Then, the slip-wall wall model is improved, in which the slip length is redefined and the Robin boundary condition is imposed at the solid wall. The improved slip-wall model is implemented in the local DFD method to evaluated the tangential velocity at an exterior dependent node, and then the requirement on high resolution of boundary layers can be alleviated. The non-equilibrium effects are accounted for by adding an explicit correction to the wall shear stress. In order to validate the present wall-modeled LES/DFD method, a series of turbulent channel flows at various Reynolds numbers, the flow over periodic hills and the flows over a NACA 4412 airfoil at a high Reynolds number are simulated. The predicted results agree well with the referenced experimental data and numerical results. Especially, the results of the separated flow over the airfoil at a near-stall condition demonstrate the performance of the present wall-modeled LES/DFD method for complex flows.
A 2D multimaterial ALE method for simulating compressible flows is presented in which a novel coupled volume of fluid and level set (VOSET) interface reconstruction method is developed for interface capturing. The novel VOSET method improves the accuracy and fidelity in interface reconstruction procedure, especially in under-resolved regions.
In this work, we present a two-dimensional multimaterial arbitrary Lagrangian–Eulerian (ALE) method for simulating compressible flows in which a novel coupled volume of fluid and level set interface reconstruction (VOSET) method is developed for interface capturing. The VOSET method combines the merits of both the volume of fluid method and the level set method by using a geometrical iterative operation. Compared to the original VOSET method, the novel VOSET method proposed in this work further improves the accuracy and fidelity in interface reconstruction procedure, especially in under-resolved regions. Several typical two-dimensional numerical experiments are presented to investigate the effectiveness of the proposed VOSET method and its performance when coupling with the multimaterial ALE solver. Numerical results demonstrate its good capability in capturing material interfaces during the simulation of compressible two-material flows.
This work presents a workflow using coupled particle methods to relate cell deformation to cell properties. Numerical results were validated with microscopic experimental data of MCF7 cancerous cell. Key findings include: (i) Stress and deformation are generally correlated, but with dependence on cell shape. (ii) Cell deformation is sensitive to flow profile, especially wall shear stress. (iii) Low cell stiffness and high flow blockage can aggravate cell deformation.
Properties of a cell can determine its deformations, which can aggravate cancer metastasis. In laboratory, microfluidic technology has been adopted to study cell deformations. However, quantifying the effects of cell deformations has remained difficult. To this end, this paper presents a two-dimensional particle-based model that can capture flow-induced cell deformations in a microchannel. The numerical model is validated with an experimental dataset for MCF7 cell. The simulations show that cell deformations are dominantly attributed to flow acceleration. Stress analyses, conducted by inputting the simulated cell deformations as boundary conditions, show that the maximum normal stresses correspond well to high deformations. Shear stress is in general proportional to the cell's distance from a wall. The simulations also suggest a deformed cell shape that apparently may reduce the average normal stresses. This study highlights the potential of the numerical model to relate the measurable cell deformations to the more elusive cell properties.
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Junming Duan, Jan S. Hesthaven
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Yufeng Wei, Yajun Zhu, Kun Xu
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Junhong Yue, Peijun Li
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Lukas Lundgren, Murtazo Nazarov
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Timothy R. Law, Philip T. Barton
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Clemens Willers, Oliver Kamps
Publication date: 15 January 2024
Source: Journal of Computational Physics, Volume 497
Author(s): Yibo Fang, Lin Du, Chen He, Dakun Sun, Lijun Yang, Qingfei Fu, Xiaofeng Sun
This paper studies the inverted stochastic lattice Boltzmann-Lagrangian approach for identifying indoor particulate pollutant sources. The dynamics of the fluid (indoor air) as well as the transport of the particles in the Eulerian description are solved using the lattice Boltzmann method. The particles regard as rigid bodies, and the data interactions between lattice fluid and particle movement are implemented by calculating for interaction force and void fraction. Particle-wall collision process is based on the softball model which describes the dynamic characteristics of particles in microscopic state. The results are shown that the particle forward and inverted drifting paths and its mechanisms are investigated clearly than previous methods. Indoor particulate pollutant sources can exactly identify with this approach. This research can offer theoretical relevance to the modeling of multi-phase particle fluid.
In this study, shock stand-off distances for thermally and chemically non-equilibrium flows of nitrogen over wedges are computationally investigated via a hypersonic computational fluid dynamics solver, hyperReactingFoam by spanning a parameter space that consists of ranges of Mach number, 4–10, specific heat ratio, 1.40–1.61 and wedge angles, 60 \(^\circ \) –90 \(^\circ \) . Then, the space is reduced into the parameters of inverse density ratio across the shock and dimensionless wedge angle which will be used as variables for quadratic functions that represent shock stand-off distances. Besides the functions of shock stand-off distances, detached shock profiles of computationally modeled flows are represented by parabolic equations. The flows are observed to be chemically frozen for Mach number ranges of 4–5 regardless of the specific heat ratio value of the nitrogen mixture. Our results show that the shock stand-off distance decreases as Mach number is increased from 4 to 7, if the wedge angle and free-stream specific heat ratio are kept the same. On the other hand, if Mach number is increased beyond 7, the shock stand-off distance starts to extend due to the dissociation of nitrogen molecules behind the shock wave. At Mach 10, nitrogen completely dissociates over 90 \(^\circ \) wedge for all specific heat ratios considered in the present study. Increased leading edge angle of the wedge or specific heat ratio of free-stream yields longer shock stand-off distance.
In simulating two-phase combustion, most Reynolds-averaged Navier–Stokes (RANS) simulation and large-eddy simulation (LES) used Eulerian–Lagrangian (E–L) modeling (Eulerian treatment of gas phase and Lagrangian treatment of particles/droplets) which needs much more computational time than the Eulerian–Eulerian (E–E) or two-fluid modeling. However, in the E–E modeling, the problem of how to reduce the computation time for poly-dispersed particles is encountered . To solve this problem, the present author proposed an Eulerian–Eulerian–Lagrangian (E–E–L) modeling of two-phase combustion for both RANS modeling and LES. The E–E–L modeling is an Eulerian treatment of gas phase and a combined Eulerian–Lagrangian treatment of particles/droplets, in which the particle velocity and concentration are solved by Eulerian modeling, and particle temperature and mass change due to reaction are solved by Lagrangian modeling. In this paper, a review is given for an E–E–L modeling of coal combustion, its application in RANS simulation and its possible application in LES. For E–E–L LES, an energy equation model of two-phase sub-grid scale (SGS) stresses accounting for the interaction between two-phase SGS stresses is suggested, and a second-order moment SGS (SOM-SGS) turbulence-chemistry model is adopted to simulate gas-phase reaction in two-phase combustion. These SGS models were separately assessed by comparison with experiments.
Flickering buoyant diffusion methane flames in weakly rotatory flows were computationally and theoretically investigated. The prominent computational finding is that the flicker frequency nonlinearly increases with the nondimensional rotational intensity R (up to 0.24), which is proportional to the nondimensional circumferential circulation. This finding is consistent with the previous experimental observations that rotatory flows enhance flame flicker to a certain extent. Based on the vortex-dynamical understanding of flickering flames that the flame flicker is caused by the periodic shedding of buoyancy-induced toroidal vortices, a scaling theory is formulated for flickering buoyant diffusion flames in weakly rotatory flows. The theory predicts that the increase of flicker frequency f obeys the scaling relation \(\left( f-f_{0} \right) \propto R^{2}\) , which agrees very well with the present computational results. In physics, the external rotatory flow enhances the radial pressure gradient around the flame, and the significant baroclinic effect \(\mathrm {\nabla }p\times \mathrm {\nabla }\rho \) contributes an additional source for the growth of toroidal vortices so that their periodic shedding is faster.
The coupling interactions between deformable structures and unsteady fluid flows occur across a wide range of spatial and temporal scales in many engineering applications. These fluid–structure interactions (FSI) pose significant challenges in accurately predicting flow physics. In the present work, two multi-layer network approaches are proposed that characterize the interactions between the fluid and structural layers for an incompressible laminar flow over a two-dimensional compliant flat plate at a 35 \(^{\circ }\) angle of attack. In the first approach, the network nodes are formed by wake vortices and bound vortexlets, and the edges of the network are defined by the induced velocity between these elements. In the second approach, coherent structures (fluid modes), contributing to the kinetic energy of the flow, and structural modes, contributing to the kinetic energy of the compliant structure, constitute the network nodes. The energy transfers between the modes are extracted using a perturbation approach. Furthermore, the network structure of the FSI system is simplified using the community detection algorithm in the vortical approach and by selecting dominant modes in the modal approach. Network measures are used to reveal the temporal behavior of the individual nodes within the simplified FSI system. Predictive models are then built using both data-driven and physics-based methods. Overall, this work sets the foundation for network-theoretic reduced-order modeling of fluid–structure interactions, generalizable to other multi-physics systems.
The paper presents a three-dimensional numerical study of the acoustic streaming induced by the dissipation of ultrasounds during their propagation in the air. The waves are generated by a circular acoustic source positioned at the center of the left wall of a parallelepipedic cavity. The simulations are performed with the lattice Boltzmann method associated with the D3Q19 multiple relaxation time model. A validation of this model is first performed by comparing the numerical and analytical acoustic intensities along the central axis of the acoustic source. The main objective of this study is to use two different methods to calculate the acoustic streaming flow. The first method is the direct calculation of the mean velocity fields as the mean values of the instantaneous velocities. The second method is an indirect technique, which first calculates the acoustic streaming force and then injects this force into the numerical code to produce the streaming. A comparison between the results obtained by the two methods was carried out and a good agreement was found between them. These different investigations, rather new in three-dimensional configurations, have allowed us to discuss the advantages and limitations of the lattice Boltzmann approach to simulate real situations of wave propagation and acoustic streaming.
Pressure-driven Newtonian fluid flow between grooved and flat surfaces is analysed with no-slip boundary conditions at walls. The effect of corrugation on the fluid flow is investigated using the mesh-free spectral method. The primary aim of the present work is to develop an asymptotic/semi-analytical theory for confined transverse flows to bridge the gap between the limits of thin and thick channels. The secondary aim is to calculate permeability with reference to the effect of wall corrugation (roughness) without the restriction of pattern amplitude. We performed mathematical modelling and evaluated the analytical solution for hydraulic permeability with respect to the flat channel. The Pad \(\acute{e}\) approximate is employed to improve the solution accuracy of an asymptotic model. The results elucidate that permeability always follows a decreasing trend with increasing pattern amplitude using the spectral approach at the long-wave and short-wave limits. The prediction of the spectral model is more accurate than the asymptotic-based model by Stroock et al. (Anal Chem 74(20):5306, 2002) and Pad \(\acute{e}\) approximate, regardless of the grooved depth and wavelength of the channel. The finite-element-based numerical simulation is also used to understand the usefulness of theoretical models. A very low computational time is required using the mesh-free spectral model as compared to the numerical study. The agreement between the present model and the fully resolved numerical results is gratifying. Regarding numerical values, we calculated the relative error for different theoretical models such as an asymptotic model, Pad \(\acute{e}\) approximate, and a mesh-free spectral model. The spectral model always predicts the maximum relative error as less than \(3 \%\) , regardless of the large pattern amplitude and wavelength. In addition, the results of the molecular dynamic (MD) simulations by Guo et al. (Phys Rev Fluids 1(7):074102, 2016) and the theoretical model by Wang (Phys Fluids 15(5):1121, 2003) are found to be quantitatively compatible with the predictions of effective slip length from the spectral model in the thick channel limit.
The aerodynamic and aeroacoustic performance of a low-aspect-ratio ( \(\hbox {AR}=0.2\) ) pitching foil during dynamic stall are investigated numerically with focus on the effects of trailing edge serrations. A hybrid method coupling an immersed boundary method for incompressible flows with the Ffowcs Williams–Hawkings acoustic analogy is employed. Large eddy simulation and turbulent boundary layer equation wall model are also employed to capture the turbulent effects. A modified NACA0012 foil with a rectangular trailing edge flap attached to the trailing edge (baseline case) undergoing pitching motion is considered. Trailing edge serrations are applied to the trailing edge flap and their effects on the aerodynamic and aeroacoustic performance of the oscillating airfoil are considered by varying the wave amplitude ( \(2h^*= 0.05, 0.1\) , and 0.2) at a Reynolds number of 100,000 and a Mach number of 0.05. It is found that the reduction of the sound pressure level at the dimensionless frequency band \(St_{b}\in [1.25,4]\) can be over 4 dB with the presence of the trailing edge serrations ( \(2h^*=0.1\) ), while the aerodynamic performance and its fluctuations are not significantly altered except a reduction around 10% in the negative moment coefficient and it fluctuations. This is due to the reduction of the average spanwise coherence function and the average surface pressure with respect to that of the baseline case, suggesting the reduction of the spanwise coherence and the noise source may result in the noise reduction. Analysis of the topology of the near wake coherent structure for \(2h^*=0.1\) reveals that the alignment of the streamwise-oriented vortex with the serration edge may reduce the surface pressure fluctuation.
We present a Graphic Processing Units (GPU) implementation of non-Newtonian Hele-Shaw flow that models the displacement of Herschel-Bulkley fluids along narrow eccentric annuli. This flow is characteristic of many long-thin flows that require extensive calculation due to an inherent nonlinearity in the constitutive law. A common method of dealing with such flows is via an augmented Lagrangian algorithm, which is often painfully slow. Here we show that such algorithms, although involving slow iterations, can often be accelerated via parallel implementation on GPUs. Indeed, such algorithms explicitly solve the nonlinear aspects only locally on each mesh cell (or node), which makes them ideal candidates for GPUs. Combined with other advances, the optimized GPU implementation takes \(\approx 2.5\%\) of the time of the original algorithm.
In the engineering field, it is necessary to construct a numerical model that can reproduce multiphase flows containing three or more phases with high accuracy. In our previous study, by extending the conservative Allen–Cahn (CAC) model, which is computationally considerably more efficient than the conventional Cahn–Hilliard (CH) model, to the multiphase flow problem with three or more phases, we developed the conservative Allen–Cahn type multi-phase-field (CAC–MPF) model. In this study, we newly construct the improved CAC–MPF model by modifying the Lagrange multiplier term of the previous CAC–MPF model to a conservative form. The accuracy of the improved CAC–MPF model is evaluated through a comparison of five models: three CAC–MPF models and two CH–MPF models. The results indicate that the improved CAC–MPF model can accurately and efficiently perform simulations of multiphase flows with three or more phases while maintaining the same level of volume conservation as the CH model. We expect that the improved CAC–MPF model will be applied to various engineering problems with multiphase flows with high accuracy.
