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16 pages, 4671 KiB

Open AccessArticle

Increasing Micro-Rotational Viscosity Results in Large Micro-Rotations: A Study Based on Monolithic Eulerian Cosserat Fluid–Structure Interaction Formulation

by Nazim Hussain Hajano, Muhammad Sabeel Khan and Lisheng Liu

Mathematics 2022, 10(22), 4188; https://doi.org/10.3390/math10224188 - 09 Nov 2022

Cited by 1 | Viewed by 1038

Abstract

In classical continuum mechanics, a monolithic Eulerian formulation is used for numerically solving fluid–structure interaction (FSI) problems in the frame of a physically deformed configuration. This numerical approach is well adapted to large-displacement fluid–structure configurations where velocities of solids and fluids are computed [...] Read more.

In classical continuum mechanics, a monolithic Eulerian formulation is used for numerically solving fluid–structure interaction (FSI) problems in the frame of a physically deformed configuration. This numerical approach is well adapted to large-displacement fluid–structure configurations where velocities of solids and fluids are computed all at once in a single variational equation. In the recent past, a monolithic Eulerian formulation for solving FSI problems of finite deformation to study the different physical features of fluid flow has been employed. Almost all the current studies use a classical framework in their approach. Despite producing decent results, such methods still need to be appropriately configured to generate exceptional results. Recently, a number of researchers have used a non-classical framework in their approach to analyze several physical problems. Therefore, in this paper, a monolithic Eulerian formulation is employed for solving FSI problems in a non-classical framework to study the micro-structural characteristics of fluid flow by validating the results with classical benchmark solutions present in the literature. In this respect, the Cosserat theory of continuum is considered where a continuum of oriented rigid particles has, in addition to the three translational degrees of freedom of classical continuum, three micro-rotational degrees of freedom. The mathematical formulation of model equations is derived from the general laws of continuum mechanics. Based on the variational formulation of the FSI system, we propose the finite element method and semi-implicit scheme for discretizing space and time domains. The results are obtained by computing a well-known classical FSI benchmark test problem FLUSTRUK-FSI-3* with FreeFem++. The results of the study indicate that the increase in micro-rotational viscosity

μ_{r}

leads to significantly large micro-rotations in fluid flow at the micro-structural level. Further, it is found that the amplitude of oscillations is related inversely to the material parameters c₁ and

μ_{r}

while the increase in c₁ stabilizes the amplitude of oscillations relatively more quickly than increasing

μ_{r .}

The color snapshots of the numerical results at different times during the computer simulations and general conclusions drawn from the results are presented. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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21 pages, 5755 KiB

Open AccessArticle

An Improved Component-Wise WENO-NIP Scheme for Euler System

by Ruo Li and Wei Zhong

Mathematics 2022, 10(20), 3881; https://doi.org/10.3390/math10203881 - 19 Oct 2022

Cited by 1 | Viewed by 1235

Abstract

As is well known, due to the spectral decomposition of the Jacobian matrix, the WENO reconstructions in the characteristic-wise fashion (abbreviated as CH-WENO) need much higher computational cost and more complicated implementation than their counterparts in the component-wise fashion (abbreviated as CP-WENO). Hence, [...] Read more.

As is well known, due to the spectral decomposition of the Jacobian matrix, the WENO reconstructions in the characteristic-wise fashion (abbreviated as CH-WENO) need much higher computational cost and more complicated implementation than their counterparts in the component-wise fashion (abbreviated as CP-WENO). Hence, the CP-WENO schemes are very popular methods for large-scale simulations or situations whose full characteristic structures cannot be obtained in closed form. Unfortunately, the CP-WENO schemes usually suffer from spurious oscillations badly. The main objective of the present work is to overcome this drawback for the CP-WENO-NIP scheme, whose counterpart in the characteristic-wise fashion was carefully studied and well-validated numerically. The approximated dispersion relation (ADR) analysis is performed to study the spectral property of the CP-WENO-NIP scheme and then a negative-dissipation interval which leads to a high risk of causing spurious oscillations is discovered. In order to remove this negative-dissipation interval, an additional term is introduced to the nonlinear weights formula of the CP-WENO-NIP scheme. The improved scheme is denoted as CP-WENO-INIP. Accuracy test examples indicate that the proposed CP-WENO-INIP scheme can achieve the optimal convergence orders in smooth regions even in the presence of the critical points. Extensive numerical experiments demonstrate that the CP-WENO-INIP scheme is much more robust compared to the corresponding CP-WENO-NIP or even CH-WENO-NIP schemes for both 1D and 2D problems modeled via the Euler equations. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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16 pages, 1980 KiB

Open AccessArticle

Numerical Simulation of Single Droplet Impingement upon Dynamic Liquid Film Obliquely

by Shanshan Yang, Quanyuan Zeng, Xiaohua Zhang, Chunzhu Dong and Ling Guan

Mathematics 2022, 10(17), 3193; https://doi.org/10.3390/math10173193 - 04 Sep 2022

Cited by 3 | Viewed by 1345

Abstract

To better understand the application of droplet impingement in industry and agriculture, in this paper, the coupled level set and volume of fluid (

C L S V O F

) method is applied to study droplet oblique impact on a dynamic liquid [...] Read more.

To better understand the application of droplet impingement in industry and agriculture, in this paper, the coupled level set and volume of fluid (

C L S V O F

) method is applied to study droplet oblique impact on a dynamic liquid film. The conclusions are the following: the downstream crown height increases and then decreases as the impact angle increases, whereas upstream crown height and spreading length decrease significantly; moreover, the spreading length and upstream crown height increase with the increase of film velocity, while the downstream crown height decreases instead. The increase of gas density inhibits both upstream and downstream crowns. When the fluid viscosity decreases or the impact velocity increases, the crown height increases significantly, which easily leads to crown rupture or droplet splash. The increase in impact velocity leads to an increase in spreading length; however, viscosity has almost no effect on the spreading length. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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12 pages, 1135 KiB

Open AccessArticle

Improved Polymer Crystal Phase Field Model and Numerical Simulation

by Binxin Yang, Zhifeng Wang and Zhijuan Meng

Mathematics 2022, 10(17), 3181; https://doi.org/10.3390/math10173181 - 03 Sep 2022

Cited by 1 | Viewed by 1021

Abstract

The existing phase field model of polymer crystallization contains many parameters that lack actual physical meaning. Although the value of these parameters can be adjusted to obtain results consistent with the experiment, it cannot correspond to the experimental conditions. In this paper, a [...] Read more.

The existing phase field model of polymer crystallization contains many parameters that lack actual physical meaning. Although the value of these parameters can be adjusted to obtain results consistent with the experiment, it cannot correspond to the experimental conditions. In this paper, a new phase field model is established. By adjusting the latent heat, various forms of isotactic polystyrene crystals, such as dendrites, spherulites, lamellas, etc., can be simulated. Latent heat refers to the heat absorbed or released by a substance from one phase to another and has important physical meaning during the solidification process. The finite difference method was used to solve the model, and then the data were used to visualize. The simulation results were consistent with the experiment. Numerical simulation results under pure diffusion conditions show that the newly established phase field model can qualitatively predict the polymer growth process and provide a theoretical basis for the preparation and optimization of high-performance polymers. In order to make the simulation result closer to the actual growth of the crystal, the flow velocity is added in the simulation to make the melt convection. Under forced convection, the simulated polymer crystal image is no longer symmetrical. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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21 pages, 1869 KiB

Open AccessArticle

Numerical Research of Dynamical Behavior in Engineering Applications by Using E–E Method

by Tiecheng Wu, Yulong Li, Dapeng Jiang and Yuxin Zhang

Mathematics 2022, 10(17), 3150; https://doi.org/10.3390/math10173150 - 02 Sep 2022

Cited by 1 | Viewed by 863

Abstract

In this research, a general numerical setting has been developed by finite volume approaching for the Eulerian–Eulerian method under OpenFOAM to provide an efficient reference for industrial bubbly flows having various geometrical characteristics under different conditions. Nine different test cases were selected from [...] Read more.

In this research, a general numerical setting has been developed by finite volume approaching for the Eulerian–Eulerian method under OpenFOAM to provide an efficient reference for industrial bubbly flows having various geometrical characteristics under different conditions. Nine different test cases were selected from chemical, nuclear, bio-processing and metallurgical engineering. We compared the predicted results with experimental findings, and the comparison proved that our implementation is correct. The numerical result has good agreement with the experimental result in most testing cases. From the analysis, we found that turbulent dispersion and drag forces were of critical importance and had to be considered in simulations. The turbulent dispersion took into account the turbulence effect, and the drag forces considered two-way coupling and ensured the good position of the Eulerian–Eulerian equations. Wall lubrication and lift forces had to be considered to solve phase fraction accumulation near walls, especially for aspect ratio pipe flows. Under other conditions, lateral forces could be neglected without any problem. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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15 pages, 2503 KiB

Open AccessArticle

Significance of the Coriolis Force on the Dynamics of Carreau–Yasuda Rotating Nanofluid Subject to Darcy–Forchheimer and Gyrotactic Microorganisms

by Bilal Ahmad, Muhammad Ozair Ahmad, Liaqat Ali, Bagh Ali, Ahmed Kadhim Hussein, Nehad Ali Shah and Jae Dong Chung

Mathematics 2022, 10(16), 2855; https://doi.org/10.3390/math10162855 - 10 Aug 2022

Cited by 6 | Viewed by 1620

Abstract

In this study, the significance of the Coriolis force on the dynamics of Carreau—Yasuda flow toward a continuously stretched surface subject to the Darcy–Forchheimer law is investigated. The nanoparticles are incorporated due to their unusual characteristics (e.g., extraordinary thermal conductivity), which are significant [...] Read more.

In this study, the significance of the Coriolis force on the dynamics of Carreau—Yasuda flow toward a continuously stretched surface subject to the Darcy–Forchheimer law is investigated. The nanoparticles are incorporated due to their unusual characteristics (e.g., extraordinary thermal conductivity), which are significant in heat exchangers and advanced nanotechnology. To avoid possible sedimentation of tiny particles, the gyrotactic microorganisms must be incorporated. The goal of this research was to find out the dynamics of three-dimensional rotational flow for nanofluids under the influence of Darcy–Forchheimer with the thermophoresis effect and motile microorganisms. The equations governing mass, momentum, and energy equations are formalized using partial derivatives, which may subsequently be transformed into dimensionless differential shapes using the personifications of apposite similarity transformations. The MATLAB application bvp4c was used in conjunction with a shooting technique to solve a nonlinear mathematical model based on ordinary differential equations. It was observed that the base fluid velocities decreased against higher input of rotation and porosity parameters; moreover, the Brownian motion and thermophoresis increased the temperature profile. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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18 pages, 1064 KiB

Open AccessArticle

Enhanced Unconditionally Positive Finite Difference Method for Advection–Diffusion–Reaction Equations

by Ndivhuwo Ndou, Phumlani Dlamini and Byron Alexander Jacobs

Mathematics 2022, 10(15), 2639; https://doi.org/10.3390/math10152639 - 27 Jul 2022

Cited by 11 | Viewed by 1599

Abstract

In this study, we develop the enhanced unconditionally positive finite difference method (EUPFD), and use it to solve linear and nonlinear advection–diffusion–reaction (ADR) equations. This method incorporates the proper orthogonal decomposition technique to the unconditionally positive finite difference method (UPFD) to reduce the [...] Read more.

In this study, we develop the enhanced unconditionally positive finite difference method (EUPFD), and use it to solve linear and nonlinear advection–diffusion–reaction (ADR) equations. This method incorporates the proper orthogonal decomposition technique to the unconditionally positive finite difference method (UPFD) to reduce the degree of freedom of the ADR equations. We investigate the efficiency and effectiveness of the proposed method by checking the error, convergence rate, and computational time that the method takes to converge to the exact solution. Solutions obtained by the EUPFD were compared with the exact solutions for validation purposes. The agreement between the solutions means the proposed method effectively solved the ADR equations. The numerical results show that the proposed method greatly improves computational efficiency without a significant loss in accuracy for solving linear and nonlinear ADR equations. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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14 pages, 6526 KiB

Open AccessArticle

CFD Analysis of Wind Distribution around Buildings in Low-Density Urban Community

by Nidhal Hnaien, Walid Hassen, Lioua Kolsi, Abdelhakim Mesloub, Mohammed A. Alghaseb, Khaled Elkhayat and Mohamed Hssan Hassan Abdelhafez

Mathematics 2022, 10(7), 1118; https://doi.org/10.3390/math10071118 - 31 Mar 2022

Cited by 12 | Viewed by 2792

Abstract

The computational fluid dynamics (CFDs) models based on the steady Reynolds-averaged Navier–Stokes equations (RANSs) using the

k - ω

two-equation turbulence model are considered in order to estimate the wind flow distribution around buildings. The present investigation developed a micro-scale city model with [...] Read more.

The computational fluid dynamics (CFDs) models based on the steady Reynolds-averaged Navier–Stokes equations (RANSs) using the

k - ω

two-equation turbulence model are considered in order to estimate the wind flow distribution around buildings. The present investigation developed a micro-scale city model with building details for the Hail area (Saudi Arabia) using ANSYS FLUENT software. Based on data from the region’s meteorological stations, the effect of wind speed (from 2 to 8 m/s) and wind direction (north, east, west, and south) was simulated. This study allows us to identify areas without wind comfort such as the corner of the building and the zones between adjacent buildings, which make this zone not recommended for placement of restaurants, pedestrian passages, or gardens. Particular attention was also paid to the highest building (Hail Tower, 67 m) in order to estimate, along the tower height, the wind speed effect on the turbulence intensity, the turbulent kinetic energy (TKE), the friction coefficient, and the dynamic pressure. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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22 pages, 1881 KiB

Open AccessArticle

Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions

by Ji Huang, Chia-Ming Fan, Jiahn-Horng Chen and Jin Yan

Mathematics 2022, 10(6), 1007; https://doi.org/10.3390/math10061007 - 21 Mar 2022

Cited by 7 | Viewed by 2750

Abstract

The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave–structure interactions. In the present study, the meshless generalized finite [...] Read more.

The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave–structure interactions. In the present study, the meshless generalized finite difference method (GFDM) together with the second-order Runge–Kutta method (RKM2) is employed to construct a fully three-dimensional (3D) meshless numerical wave flume (NWF). Three numerical examples, i.e., the propagation of freak waves, irregular waves and focused waves, are implemented to verify the accuracy and stability of the developed 3D GFDM model. The results show that the present numerical model possesses good performance in the simulation of nonlinear water waves and suggest that the 3D “RKM2-GFDM” meshless scheme can be adopted to further simulate more complex nonlinear problems regarding wave–structure interactions in ocean engineering. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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Review

Jump to: Research

18 pages, 2187 KiB

Open AccessReview

A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations

by Min Wang and Xiaohua Zhang

Mathematics 2022, 10(9), 1482; https://doi.org/10.3390/math10091482 - 29 Apr 2022

Viewed by 1292

Abstract

The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the [...] Read more.

The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness. Full article

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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