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An Accurate, Robust and Efficient Convection-Pressure Flux Splitting Scheme for Compressible Euler Flows

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SSRN

SSRN 2023年

作者： Hu, Lijun Tan, Shide Li, Long Yuan, Haizhuan School of Mathematics and Statistics Hengyang Normal University Hunan Hengyang421002 China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan Xiangtan411105 China

The Roe's flux difference splitting scheme has been a popular shock-capturing method in computational fluid dynamics due to its high resolution for various discontinuities. However, it fails to satisfy the entropy condition and will encounter different forms of instability while calculating shock wave problems, such as the occurrence of post-shock oscillation in simulations of slowly moving shock waves and the carbuncle phenomenon in simulations of multidimensional strong shock waves. A simple flux difference splitting scheme based on the idea of convection-pressure splitting is proposed in the present work. The flux of the 3D Euler equations is split into the convection part and the pressure part with application of the Toro-Vazquez splitting procedure. The pressure subsystem has a complete set of linearly independent eigenvectors and thus it is solved by the conventional flux difference splitting method which is based on the eigenstructure of the system. The weakly hyperbolic convection subsystem, however, does not have a complete set of linearly independent eigenvectors and it is solved by the flux difference splitting scheme based on the generalized eigenvectors. In order to improve the resolution for contact discontinuities, a strategy combining the THINC reconstruction with the BVD algorithm is employed to minimize the density difference in the numerical dissipation term of the convection flux. Results of stability analysis show that the proposed scheme can effectively attenuate the numerical error and thus suppress the multidimensional shock instability. A comprehensive range of numerical simulations for classical 1D, 2D and 3D benchmark test problems demonstrate that the proposed scheme satisfies the entropy condition and positivity-preserving, possesses high resolution for contact discontinuities, and, more importantly, is free from the post-shock oscillation of slowly moving shock waves and the instability of multidimensional strong shock waves. © 2023, Th

关键词： Eigenvalues and eigenfunctions

Two-Relaxation-Time Regularized Lattice Boltzmann Model for Navier-Stokes Equations

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SSRN

SSRN 2024年

作者： Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan aSchool of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China bNational Center for Applied Mathematics in Hunan Xiangtan 411105 China cHunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan 411105 China

In this paper, we propose a novel two-relaxation-time regularized lattice Boltzmann (TRTRLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, τs,2, is employed to relax the regularized non-equilibrium third-order terms. ChapmanEnskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as Re = 107. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model’s capability to accurately compute ultra-low Reynolds numbers as Re = 10−7. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics. © 2024, The Authors. All rights reserved.

关键词： Navier Stokes equations

A posteriori error estimation for an interior penalty virtual element method of Kirchhoff plates

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arXiv 2024年

作者： Feng, Fang Hu, Yuming Yu, Yue Zhao, Jikun School of Mathematics and Statistics Nanjing University of Science and Technology Nanjing China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China School of Mathematics and Statistics Zhengzhou University Zhengzhou450001 China

In this paper, we develop a residual-type a posteriori error estimation for an interior penalty virtual element method (IPVEM) for the Kirchhoff plate bending problem. Building on the work in [18], we adopt a modified discrete variational formulation that incorporates the H1-elliptic projector in the jump and average terms. This allows us to simplify the numerical implementation by including the H1-elliptic projector in the computable error estimators. We derive the reliability and efficiency of the a posteriori error bound by constructing an enriching operator and establishing some related error estimates that align with C0-continuous interior penalty finite element methods. As observed in the a priori analysis, the interior penalty virtual elements exhibit similar behaviors to C0continuous elements despite its discontinuity. This observation extends to the a posteriori estimate since we do not need to account for the jumps of the function itself in the discrete scheme and the error estimators. As an outcome of the error estimator, an adaptive VEM is introduced by means of the mesh refinement strategy with the one-hanging-node rule. Numerical results from several benchmark tests confirm the robustness of the proposed error estimators and show the efficiency of the resulting adaptive VEM. Copyright © 2024, The Authors. All rights reserved.

关键词： Discrete element methods

Paired 2-Disjoint Path Covers of Burnt Pancake Graphs with Faulty Elements

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SSRN

SSRN 2024年

作者： Li, Pingshan Chen, Congzhen Liu, Xianglin Xiangtan University China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China Key Laboratory of Intelligent Computing & Information Processing of Education China Key Laboratory for Computation and Simulation in Science and Engineering China National Center for Applied Mathematics in Hunan China Guangxi Vocational University of Agriculture Guangxi Nanning530007 China

It is a key issue in parallel processing to find $k$-disjoint paths in the underlying graph of an interconnected network such that these disjoint paths pass through all vertices of the network, this is known as paired $k$-disjoint path cover problems or unpaired $k$-disjoint path cover problems. In 2024, Dvo\v{r}\'{a}k and Gu (Theoretical Computer Science, $986 (2024) 114327$) showed that there exist two disjoint paths whose vertices partition the vertex of the burnt pancake graph even if it contains at most $n-4$ faulty elements (vertices or edges) and they proposed an open problem: is it possible to improve the upper bound $n-4$ to $n-3$? In this paper, we provide a positive answer to this problem. © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with variable coefficients

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arXiv 2023年

作者： Yu, Yuan Qin, Zuojian Yuan, Haizhuan Shu, Shi School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for convection-diffusion equation (CDE) with variable coefficients is proposed. Within this framework, we first derive a TRT-R collision operator by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium. Then a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally and most importantly, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE with variable coefficients. To evaluate this model, we simulate a classic benchmark problem of the rotating Gaussian pulse. The results show that our model has better accuracy, stability and convergence than other popular LB models, especially in the case of a large time step. Copyright © 2023, The Authors. All rights reserved.

关键词： Boltzmann equation

Two-relaxation-time regularized lattice Boltzmann model for Navier-Stokes equations

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arXiv 2023年

作者： Yu, Yuan Qin, Zuojian Chen, Siwei Shu, Shi Yuan, Hai-Zhuan School of Mathematics and Computational Science Xiangtan University Xiangtan411105 China National Center for Applied Mathematics in Hunan Xiangtan411105 China Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Xiangtan411105 China

In this paper, we develop a two-relaxation-time regularized lattice Boltzmann (TRT-RLB) model for simulating weakly compressible isothermal flows. A free relaxation parameter, τs,2, is employed to relax the regularized non-equilibrium third-order terms. Chapman-Enskog analysis reveals that our model can accurately recover the Navier-Stokes equations (NSEs). Theoretical analysis of the Poiseuille flow problem demonstrates that the slip velocity magnitude in the proposed model is controlled by a magic parameter, which can be entirely eliminated under specific values, consistent with the classical TRT model. Our simulations of the double shear layer problem, Taylor-Green vortex flow, and force-driven Poiseuille flow confirm that the stability and accuracy of our model significantly surpass those of both the regularized lattice Boltzmann (RLB) and two-relaxation-time (TRT) models, even under super-high Reynolds numbers as Re = 107. Concurrently, the TRT-RLB model exhibits superior performance in very high viscosity scenarios. The simulations of creeping flow around a square cylinder demonstrates the model's capability to accurately compute ultra-low Reynolds numbers as Re = 10−7. This study establishes the TRT-RLB model as a flexible and robust tool in computational fluid dynamics. Copyright © 2023, The Authors. All rights reserved.

关键词： Navier Stokes equations

Achieving coherent perfect absorption based on flat-band plasmonic Friedrich-Wintgen BIC in borophene metamaterials

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arXiv 2023年

作者： Zhang, Yan-Xi Lin, Qi Yan, Xiao-Qiang Wang, Ling-Ling Liu, Gui-Dong School of Physics and Optoelectronics Xiangtan University Xiangtan411105 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan University Hunan411105 China School of Physics and Electronics Hunan University Changsha410082 China

Many applications involve the phenomenon of a material absorbing electromagnetic radiation. By exploiting wave interference, the efficiency of absorption can be significantly enhanced. Here, we propose Friedrich-Wintgen bound states in the continuum (F-W BICs) based on borophene metamaterials to realize coherent perfect absorption with a dual-band absorption peak in commercially important communication bands. The metamaterials consist of borophene gratings and a borophene sheet that can simultaneously support a Fabry-Perot plasmon resonance and a guided plasmon mode. The formation and dynamic modulation of the F-W BIC can be achieved by adjusting the width or carrier density of the borophene grating, while the strong coupling leads to the anti-crossover behavior of the absorption spectrum. Due to the weak angular dispersion originating from the intrinsic flat-band characteristic of the deep sub-wavelength periodic structure, the proposed plasmonic system exhibits almost no change in wavelength and absorption at large incident angles (within 70 degrees). In addition, we employ the temporal coupled-mode theory including near- and far-field coupling to obtain strong critical coupling, successfully achieve coherent perfect absorption, and can realize the absorption switch by changing the phase difference between the two coherent beams. Our findings can offer theoretical support for absorber design and all-optical tuning. Copyright © 2023, The Authors. All rights reserved.

关键词： Absorption spectroscopy

Multitask kernel-learning parameter prediction method for solving time-dependent linear systems

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arXiv 2022年

作者： Jiang, Kai Zhang, Juan Zhou, Qi Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Matrix splitting iteration methods play a vital role in solving large sparse linear systems. Their performance heavily depends on the splitting parameters, however, the approach of selecting optimal splitting parameters has not been well developed. In this paper, we present a multitask kernel-learning parameter prediction method to automatically obtain relatively optimal splitting parameters, which contains simultaneous multiple parameters prediction and a data-driven kernel learning. For solving time-dependent linear systems, including linear differential systems and linear matrix systems, we give a new matrix splitting Kronecker product method, as well as its convergence analysis and preconditioning strategy. Numerical results illustrate our methods can save an enormous amount of time in selecting the relatively optimal splitting parameters compared with the exists methods. Moreover, our iteration method as a preconditioner can effectively accelerate GMRES. As the dimension of systems increases, all the advantages of our approaches becomes significantly. Especially, for solving the differential Sylvester matrix equation, the speedup ratio can reach tens to hundreds of times when the scale of the system is larger than one hundred thousand. Copyright © 2022, The Authors. All rights reserved.

关键词： Linear systems

A general alternating-direction implicit Newton method for solving complex continuous-time algebraic Riccati matrix equation

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arXiv 2022年

作者： Li, Shifeng Jiang, Kai Zhang, Juan Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

In this paper, applying the Newton method, we transform the complex continuous-time algebraic Riccati matrix equation into a Lyapunov equation. Then, we introduce an efficient general alternating-direction implicit (GADI) method to solve the Lyapunov equation. The inexact Newton-GADI method is presented to save computational amount effectively. Moreover, we analyze the convergence of the Newton-GADI method. The convergence rate of the Newton-GADI and Newton-ADI methods is compared by analyzing their spectral radii. Furthermore, we give a way to select the quasi-optimal parameter. Corresponding numerical tests are shown to illustrate the effectiveness of the proposed algorithms. © 2022, CC BY-SA.

关键词： Newton-Raphson method