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Guo W, Hou G. Novel Schemes of No-Slip Boundary Conditions for the Discrete Unified Gas Kinetic Scheme Based on the Moment Constraints. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25050780. [PMID: 37238535 DOI: 10.3390/e25050780] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2023] [Revised: 05/08/2023] [Accepted: 05/09/2023] [Indexed: 05/28/2023]
Abstract
The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole-wall collision, and Rayleigh-Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole-wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh-Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS.
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Affiliation(s)
- Wenqiang Guo
- Hypervelocity Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China
- Laboratory of Aerodynamics in Multiple Flow Regimes, China Aerodynamics Research and Development Center, Mianyang 621000, China
- School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Guoxiang Hou
- School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
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Yang Z, Liu S, Zhuo C, Zhong C. Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1202. [PMID: 36141088 PMCID: PMC9498057 DOI: 10.3390/e24091202] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/02/2022] [Revised: 08/21/2022] [Accepted: 08/24/2022] [Indexed: 06/16/2023]
Abstract
The multiphase model based on free-energy theory has been experiencing long-term prosperity for its solid foundation and succinct implementation. To identify the main hindrance to developing a free-energy-based discrete unified gas-kinetic scheme (DUGKS), we introduced the classical lattice Boltzmann free-energy model into the DUGKS implemented with different flux reconstruction schemes. It is found that the force imbalance amplified by the reconstruction errors prevents the direct application of the free-energy model to the DUGKS. By coupling the well-balanced free-energy model with the DUGKS, the influences of the amplified force imbalance are entirely removed. Comparative results demonstrated a consistent performance of the well-balanced DUGKS despite the reconstruction schemes utilized. The capability of the DUGKS coupled with the well-balanced free-energy model was quantitatively validated by the coexisting density curves and Laplace's law. In the quiescent droplet test, the magnitude of spurious currents is reduced to a machine accuracy of 10-15. Aside from the excellent performance of the well-balanced DUGKS in predicting steady-state multiphase flows, the spinodal decomposition test and the droplet coalescence test revealed its stability problems in dealing with transient flows. Further improvements are required on this point.
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Affiliation(s)
- Zeren Yang
- School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
| | - Sha Liu
- School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an 710072, China
| | - Congshan Zhuo
- School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an 710072, China
| | - Chengwen Zhong
- School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an 710072, China
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Lin C, Luo KH, Xu A, Gan Y, Lai H. Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects. Phys Rev E 2021; 103:013305. [PMID: 33601619 DOI: 10.1103/physreve.103.013305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2020] [Accepted: 12/16/2020] [Indexed: 06/12/2023]
Abstract
A multiple-relaxation-time discrete Boltzmann model (DBM) is proposed for multicomponent mixtures, where compressible, hydrodynamic, and thermodynamic nonequilibrium effects are taken into account. It allows the specific heat ratio and the Prandtl number to be adjustable, and is suitable for both low and high speed fluid flows. From the physical side, besides being consistent with the multicomponent Navier-Stokes equations, Fick's law, and Stefan-Maxwell diffusion equation in the hydrodynamic limit, the DBM provides more kinetic information about the nonequilibrium effects. The physical capability of DBM to describe the nonequilibrium flows, beyond the Navier-Stokes representation, enables the study of the entropy production mechanism in complex flows, especially in multicomponent mixtures. Moreover, the current kinetic model is employed to investigate nonequilibrium behaviors of the compressible Kelvin-Helmholtz instability (KHI). The entropy of mixing, the mixing area, the mixing width, the kinetic and internal energies, and the maximum and minimum temperatures are investigated during the dynamic KHI process. It is found that the mixing degree and fluid flow are similar in the KHI process for cases with various thermal conductivity and initial temperature configurations, while the maximum and minimum temperatures show different trends in cases with or without initial temperature gradients. Physically, both heat conduction and temperature exert slight influences on the formation and evolution of the KHI morphological structure.
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Affiliation(s)
- Chuandong Lin
- Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China
| | - Kai H Luo
- Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom
| | - Aiguo Xu
- Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009-26, Beijing 100088, China
- State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
- Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, China
| | - Yanbiao Gan
- North China Institute of Aerospace Engineering, Langfang 065000, China
| | - Huilin Lai
- College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350007, China
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Chen L, Succi S, Cai X, Schaefer L. Semi-Lagrangian implicit Bhatnagar-Gross-Krook collision model for the finite-volume discrete Boltzmann method. Phys Rev E 2020; 101:063301. [PMID: 32688570 DOI: 10.1103/physreve.101.063301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2019] [Accepted: 04/22/2020] [Indexed: 11/07/2022]
Abstract
In order to increase the accuracy of temporal solutions, reduce the computational cost of time marching, and improve the stability associated with collisions for the finite-volume discrete Boltzmann method, an advanced implicit Bhatnagar-Gross-Krook (BGK) collision model using a semi-Lagrangian approach is proposed in this paper. Unlike existing models, in which the implicit BGK collision is resolved either by a temporal extrapolation or by a variable transformation, the proposed model removes the implicitness by tracing the particle distribution functions (PDFs) back in time along their characteristic paths during the collision process. An interpolation scheme is needed to evaluate the PDFs at the traced-back locations. By using the first-order interpolation, the resulting model allows for the straightforward replacement of f_{α}^{eq,n+1} by f_{α}^{eq,n} no matter where it appears. After comparing the proposed model with the existing models under different numerical conditions (e.g., different flux schemes and time-marching schemes) and using the proposed model to successfully modify the variable transformation technique, three conclusions can be drawn. First, the proposed model can improve the accuracy by almost an order of magnitude. Second, it can slightly reduce the computational cost. Therefore, the proposed scheme improves accuracy without extra cost. Finally, the proposed model can significantly improve the Δt/τ limit compared to the temporal interpolation model while having the same Δt/τ limit as the variable transformation approach. The proposed scheme with a second-order interpolation is also developed and tested; however, that technique displays no advantage over the simple first-order interpolation approach. Both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first-order interpolation can outperform the same scheme with second-order interpolation, as well as the existing temporal extrapolation and variable transformation schemes.
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Affiliation(s)
- Leitao Chen
- Department of Mechanical Engineering, Rice University, Houston, Texas 77005, USA
| | - Sauro Succi
- Center for Life Nanoscience at La Sapienza, Italian Institute of Technology, 00161, Rome, Italy
| | - Xiaofeng Cai
- Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA
| | - Laura Schaefer
- Department of Mechanical Engineering, Rice University, Houston, Texas 77005, USA
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Shan B, Wang P, Zhang Y, Guo Z. Discrete unified gas kinetic scheme for all Knudsen number flows. IV. Strongly inhomogeneous fluids. Phys Rev E 2020; 101:043303. [PMID: 32422810 DOI: 10.1103/physreve.101.043303] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2019] [Accepted: 03/02/2020] [Indexed: 11/07/2022]
Abstract
This work is an extension of the discrete unified gas kinetic scheme (DUGKS) from rarefied gas dynamics to strongly inhomogeneous dense fluid systems. The fluid molecular size can be ignored for dilute gases, while the nonlocal intermolecular collisions and the competition of solid-fluid and fluid-fluid interactions play an important role for surface-confined fluid flows at the nanometer scale. The nonequilibrium state induces strong fluid structural-confined inhomogeneity and anomalous fluid flow dynamics. According to the previous kinetic model [Guo et al., Phys. Rev. E 71, 035301(R) (2005)10.1103/PhysRevE.71.035301], the long-range intermolecular attraction is modeled by the mean-field approximation, and the volume exclusion effect is considered by the hard-sphere potential in the collision operator. The kinetic model is solved by the DUGKS, which has the characteristics of asymptotic preserving, low dissipation, second-order accuracy, and multidimensional nature. Both static fluid structure and dynamic flow behaviors are calculated and validated with Monte Carlo or molecular dynamics results. It is shown that the flow of dense fluid systems tends to that of rarefied gases as the dense degree decreases or the mean flow path increases. The DUGKS is proved to be applicable to simulate such nonequilibrium dense fluid systems.
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Affiliation(s)
- Baochao Shan
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, Hubei 430000, China
| | - Peng Wang
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, Hubei 430000, China
| | - Yonghao Zhang
- James Weir Fluids Laboratory, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, United Kingdom
| | - Zhaoli Guo
- State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, Hubei 430000, China
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Yang Z, Zhong C, Zhuo C. Phase-field method based on discrete unified gas-kinetic scheme for large-density-ratio two-phase flows. Phys Rev E 2019; 99:043302. [PMID: 31108650 DOI: 10.1103/physreve.99.043302] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Indexed: 11/07/2022]
Abstract
In this paper, a phase-field method under the framework of discrete unified gas-kinetic scheme (DUGKS) for incompressible multiphase fluid flows is proposed. Two kinetic models are constructed to solve the conservative Allen-Cahn equation that accounts for the interface behavior and the incompressible hydrodynamic equations that govern the flow field, respectively. With a truncated equilibrium distribution function as well as a temporal derivative added to the source term, the macroscopic governing equations can be exactly recovered from the kinetic models through the Chapman-Enskog analysis. Calculation of source terms involving high-order derivatives existed in the quasi-incompressible model is simplified. A series of benchmark cases including four interface-capturing tests and four binary flow tests are carried out. Results compared to that of the lattice Boltzmann method (LBM) have been obtained. A convergence rate of second order can be guaranteed in the test of interface diagonal translation. The capability of the present method to track the interface that undergoes a severe deformation has been verified. Stationary bubble and spinodal decomposition problems, both with a density ratio as high as 1000, are conducted and reliable solutions have been provided. The layered Poiseuille flow with a large viscosity ratio is simulated and numerical results agree well with the analytical solutions. Variation of positions of the bubble front and spike tip during the evolution of Rayleigh-Taylor instability has been predicted precisely. However, the detailed depiction of complicated interface patterns appearing during the evolution process is failed, which is mainly caused by the relatively large numerical dissipation of DUGKS compared to that of LBM. A high-order DUGKS is needed to overcome this problem.
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Affiliation(s)
- Zeren Yang
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Chengwen Zhong
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
| | - Congshan Zhuo
- National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
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