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Chemical Reaction and Viscous Dissipative Effects on Buongiorno’s Nanofluid Model Past an Inclined Plane: A Numerical Investigation

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International Journal of applied and Computational mathematics 2024年第2期10卷 1-20页

作者： Reddy, Ramesh Gaffar, S. Abdul Department of Mathematics Madanapalle Institute of Technology & amp Preparatory Studies Center Mathematics and Computing Skills Unit University of Technology and Applied Sciences Salalah Oman

The use of nanofluid in thermal applications dramatically enhanced the pattern of heat and mass transmission, which is essential in numerous engineering and industrial areas. Numerous innovative applications in solar energy and thermal engineering can be attributed to the consideration of nanofluid. Additionally, motile microorganisms, which have applications in enzymes, bioengineering, biomedicine, biofuels and petroleum sciences, perfectly improve the stability of nanofluid. The study of nanofluid has several dynamic applications in renewable energy and thermodynamic engineering problems. The aim of this paper is to discuss the chemical viscous dissipative transport of Buongiorno’s nanofluid across an inclined plane, considering Brownian movement and thermophoresis effects. The governing equations and the associated boundary conditions are normalized using the non-similarity transformation approach. The key variables and corresponding non-similarity solutions are provided to summarize the transpiration parameters. The Keller’s Box method is used to obtain the mathematical solutions. The numerical findings are given for various thermos-physical parameter values both physically and quantitatively. The graphical effects of various thermos-physical factors on momentum, energy, nanoparticle volume fraction concentration, shear stress rate, heat and mass transfer rates are examined and well discussed. The results show strong associations when compared to previously published literature. A slight increase in velocity with a rise in Kr values. Whereas, a slight decrease in temperature with an increase in Kr values and a strong decrease in nanoparticle volume fraction concentration with an increase in Kr values. A significant increase in velocity and temperature is seen with an increase in Ec and Nb values while nanoparticle volume fraction concentration is seen to decrease slightly. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： Chemical reaction Heat transfer rate Keller’s box technique Mass transfer rate Nanofluid Skin friction Viscous dissipation

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NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

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Journal of Computational mathematics 2024年第3期42卷 851-884页

作者： Wei Liu Ziqing Xie Wenfan Yi South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China Key Laboratory of Computing and Stochastic Mathematics(Ministry of Education) Hunan Normal UniversityChangshaHunan 410081China Hunan Provincial Key Laboratory of Intelligent Information Processing and Applied Mathematics School of MathematicsHunan UniversityChangshaHunan 410082China

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert *** to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less ***,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is *** feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative ***,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each ***,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary *** numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

关键词： Multiple saddle points Local minimax method Barzilai-Borwein gradient method Normalized nonmonotone search strategy Global convergence

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A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION

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Journal of Computational mathematics 2024年第4期42卷 999-1031页

作者： Jiaofen Li Lingchang Kong Xuefeng Duan Xuelin Zhou Qilun Luo School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuangxi Key Laboratory of Automatic Detecting Technology and InstrumentsGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematical Sciences South China Normal UniversityGuangzhou 510000China School of Mathematics and Computing Science Guilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computing Science Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematics and Statistics Yunan UniversityKunming 650000China

The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,*** this paper,the original truncated complex singular value decomposition problem is formulated as a Riemannian optimiza-tion problem on a product of two complex Stiefel manifolds,a practical algorithm based on the generic Riemannian trust-region method of Absil et *** presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence *** experiments are provided to illustrate the efficiency of the proposed *** with some classical Riemannian gradient-type methods,the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB,and some latest infeasible methods for solving manifold optimization problems,are also provided to show the merits of the proposed approach.

关键词： Truncated singular value decomposition Riemannian optimization Trust-region method

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Characterizations of Weighted Besov Spaces with Variable Exponents

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Acta Mathematica Sinica,English Series 2024年第11期40卷 2855-2878页

作者： Sheng Rong WANG Peng Fei GUO Jing Shi XU School of Mathematics and Statistics Hainan Normal UniversityHaikou571158P.R.China Center for Applied Mathematics of Guangxi Guangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationSchool of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin541004P.R.China

In this paper,we first give characterizations of weighted Besov spaces with variable exponents via Peetre’s maximal *** we obtain decomposition characterizations of these spaces by atom,molecule and *** an applicatio... 详细信息

关键词： Besov space Muckenhoupt weight variable exponent Peetre’s maximal function atom molecule wavelet pseudo-differential operator

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A low Mach number asymptotic analysis of dissipation-reducing methods for curing shock instability

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applied mathematics and Mechanics(English Edition) 2025年第4期46卷 723-744页

作者： Hongping GUO Xun WANG Zhijun SHEN National Key Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing100088China Faculty of Mathematics Baotou Teachers’CollegeBaotouInner Mongolia Autonomous Region014030China School of Mathematical Sciences Peking UniversityBeijing100871China PKU-Changsha Institute for Computing and Digital Economy Changsha410205China Center for Applied Physics and Technology Peking UniversityBeijing100871China

We are intrigued by the issues of shock instability,with a particular emphasis on numerical schemes that address the carbuncle phenomenon by reducing dissipation rather than increasing *** a specific class of planar flow fields where the transverse direction exhibits vanishing but non-zero velocity components,such as a disturbed onedimensional(1D)steady shock wave,we conduct a formal asymptotic analysis for the Euler system and associated numerical *** analysis aims to illustrate the discrepancies among various low-dissipative numerical ***,a numerical stability analysis of steady shock is undertaken to identify the key factors underlying shock-stable *** verify the stability mechanism,a consistent,low-dissipation,and shock-stable HLLC-type Riemann solver is presented.

关键词： Riemann solver numerical shock instability low Mach number HLLC

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Hybrid Dynamic Mesh Redistribution – Immersed Boundary Method for Acoustic Simulation of Flow Around a Propeller

Supercomputing Frontiers and Innovations

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Supercomputing Frontiers and Innovations 2022年第4期9卷 69-84页

作者： Bobkov, Vladimir G. Kozubskaya, Tatiana K. Kudryavtseva, Liudmila N. Tsvetkova, Valeriia O. Keldysh Institute of Applied Mathematics Moscow Russia Dorodnicyn Computing Center FRC CSC RAS Moscow Russia

A novel hybrid dynamic mesh redistribution – immersed boundary method for simulation of turbulent flows around rotating obstacles of complex geometry and analysis of tonal acoustics is proposed. The feasibility of the approach is demonstrated by considering a drone propeller problem. The results of three-dimensional Reynolds-averaged Navier–Stokes simulations using the proposed approach are compared to the results of body-fitted unstructured simulations in noninertial reference frame. The dynamic mesh redistribution method allows the reposition of mesh points taking into account the shape of the moving body while retaining the mesh topology. The cell size and quality of the dynamically redistributed mesh strongly depend on the curvature of the body surface. The position and shape of the moving obstacle is prescribed by a distance function defined on an adaptive octree. The results of simulations using the proposed method are in good agreement with both the results of body-fitted simulations and the experimental data © The Authors 2022. This paper is published with open access at ***

关键词： Drones

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MONOTONICITY CORRECTIONS FOR NINE-POINT SCHEME OF DIFFUSION EQUATIONS

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Journal of Computational mathematics 2024年第5期42卷 1305-1327页

作者： Wang Kong Zhenying Hong Guangwei Yuan Zhiqiang Sheng School of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106China Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA) MIITNanjing 211106China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China

In this paper,we present a nonlinear correction technique to modify the nine-point scheme proposed in[SIAM ***.,30:3(2008),1341-1361]such that the resulted scheme preserves the *** first express the flux by the cell-centered unknowns and edge unknowns based on the stencil of the nine-point ***,we use a nonlinear combination technique to get a monotone *** order to obtain a cell-centered finite volume scheme,we need to use the cell-centered unknowns to locally approximate the auxiliary *** present a new method to approximate the auxiliary unknowns by using the idea of an improved multi-points flux *** numerical results show that the new proposed scheme is robust,can handle some distorted grids that some existing finite volume schemes could not handle,and has higher numerical accuracy than some existing positivity-preserving finite volume schemes.

关键词： Monotonicity corrections Diffusion equation Improved MPFA Distorted meshes

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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

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应用数学与计算数学学报 2025年第1期7卷 3-39页

作者： Hendrik Ranocha Andrew R.Winters Hugo Guillermo Castro Lisandro Dalcin Michael Schlottke-Lakemper Gregor J.Gassner Matteo Parsani Applied Mathematics University of HamburgBundesstr.5520146 HamburgGermany Department of Mathematics Applied Mathematics Linköping UniversityLinköpingSweden Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Applied and Computational Mathematics RWTH Aachen UniversityAachenGermany High-Performance Computing Center Stuttgart University of StuttgartStuttgartGermany Department of Mathematics and Computer Science University of CologneCologneGermany Center for Data and Simulation Science University of CologneCologneGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Physical Science and Engineering Division(PSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.

关键词： Explicit Runge-Kutta(RK)methods Step size control Compressible fluid dynamics Adaptivity in space and time Shock capturing

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The VEM for time-harmonic Maxwell equations in inhomogeneous media with Lipschitz interface

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Mathematical Models and Methods in applied Sciences 2025年第8期35卷 1717-1761页

作者： Chen, Chunyu Guo, Ruchi Wei, Huayi School of Mathematics and Computational Science Xiangtan University Xiangtan 411105 China National Center for Applied Mathematics in Hunan Xiangtan 411105 China Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Xiangtan 411105 China School of Mathematics Sichuan University Sichuan Chengdu China

It has been extensively studied in the literature that solving Maxwell equations is very sensitive to mesh structures, space conformity and solution regularity. Roughly speaking, for almost all the methods in the literature, optimal convergence for low-regularity solutions heavily relies on conforming spaces and highly regular simplicial meshes. This can be a significant limitation for many popular methods based on broken spaces and nonconforming or polytopal meshes often used for inhomogeneous media, as the discontinuity of electromagnetic parameters can lead to quite low regularity of solutions near media interfaces. This very issue can be potentially worsened by geometric singularities, making those methods particularly challenging to apply. In this paper, we present a lowest-order virtual element method for solving an indefinite time-harmonic Maxwell equation in 2D inhomogeneous media with quite arbitrary polytopal meshes, and the media interface is allowed to have geometric singularity to cause low regularity. We employ the “virtual mesh” technique originally invented in [S. Cao, L. Chen and R. Guo, A virtual finite element method for two-dimensional Maxwell interface problems with a background unfitted mesh, Math. Models Methods Appl. Sci. 31 (2021) 2907–2936] for error analysis. This work admits three key novelties: (i) the proposed method is theoretically guaranteed to achieve robust optimal convergence for solutions with merely H^θ regularity, θ ∈ (1/2, 1];(ii) the polytopal element shape can be highly anisotropic and shrinking, and an explicit formula is established to describe the relationship between the shape regularity and solution regularity;(iii) we show that the stabilization term is needed to produce optimal convergent solutions for indefinite problems. Extensive numerical experiments will be given to demonstrate the effectiveness of the proposed method. © 2025 World Scientific Publishing Company.

关键词： anisotropic analysis interface problems maximum angle conditions polygonal meshes Time-harmonic Maxwell equations virtual element methods

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Error Exponent and Strong Converse for Quantum Soft Covering

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IEEE Transactions on Information Theory 2024年第5期70卷 3499-3511页

作者： Cheng, Hao-Chung Gao, Li The Graduate Institute of Communication Engineering The Institute of Applied Mathematical Sciences National Taiwan University Center for Quantum Science and Engineering The Department of Electrical Engineering The Department of Mathematics Taipei10617 Taiwan National Center for Theoretical Sciences Physics Division Taipei10617 Taiwan Quantum Computing Center New Taipei City236 Taiwan University of Houston Department of Mathematics HoustonTX77204 United States

How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem, which uses a pairwise-independent random codebook to approximate the target output state of a quantum channel. We establish a one-shot error exponent bound and a one-shot strong converse bound on the approximation error measured in terms of the expected trace distance between the codebook-induced state and the true channel output state. When using independent and identically-distributed random codebook with a rate above the quantum mutual information I(X:B)ρ , we prove that the error decays exponentially with its error exponent expressed by the sandwiched Rényi information. On the other hand, when the rate of the codebook size is below the quantum mutual information, the error converges to one exponentially fast. Similar results are obtained using a random constant composition codebook, whereas the sandwiched Augustin information gives the error exponent. In addition to the above large deviation analysis, our results also hold in the moderate deviation regime. © 1963-2012 IEEE.

关键词： Signal encoding

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