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A Parallel Finite Element Discretization Algorithm Based on Grad-Div Stabilization for the Navier–Stokes Equations 基于纳维-斯托克斯方程 Grad-Div 稳定的并行有限元离散化算法
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-05-04 DOI: 10.1007/s00021-024-00868-1
Yueqiang Shang, Jiali Zhu, Bo Zheng
{"title":"A Parallel Finite Element Discretization Algorithm Based on Grad-Div Stabilization for the Navier–Stokes Equations","authors":"Yueqiang Shang,&nbsp;Jiali Zhu,&nbsp;Bo Zheng","doi":"10.1007/s00021-024-00868-1","DOIUrl":"10.1007/s00021-024-00868-1","url":null,"abstract":"<div><p>We present and study a parallel grad-div stabilized finite element discretization algorithm based on entire-overlapping domain decomposition for the numerical simulation of Navier–Stokes equations. The algorithm is easy to implement on top of existing sequential software, in which each subproblem used to calculate a local solution in its designated subregion is actually a global problem with vast of degrees of freedom coming from its own subregion, and hence, can be solved independently with other subproblems. We derive error bounds of the approximate solution by employing the technical tool of local a priori estimate, and investigate the effect of grad-div stabilization term on the approximation solutions. Numerical comparisons, with both inf-sup stable and unstable mixed finite elements pairs for the velocity and pressure, show that our present algorithm has an amazing superiority to its counterpart without stabilization in the sense that accuracy of the approximate velocities could be improved by two orders of magnitude when the viscosity <span>(nu )</span> is small. While compared with the usual standard serial grad-div stabilized finite element method, our algorithm saves lots of CPU time in computing a solution with comparable accuracy.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Well-Posedness of Classical Solutions to the Compressible Navier–Stokes–Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains 三维有界域中带有滑动边界条件的可压缩纳维-斯托克斯-泊松方程经典解的全局良好假设性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-05-02 DOI: 10.1007/s00021-024-00875-2
Yazhou Chen, Bin Huang, Xiaoding Shi
{"title":"Global Well-Posedness of Classical Solutions to the Compressible Navier–Stokes–Poisson Equations with Slip Boundary Conditions in 3D Bounded Domains","authors":"Yazhou Chen,&nbsp;Bin Huang,&nbsp;Xiaoding Shi","doi":"10.1007/s00021-024-00875-2","DOIUrl":"10.1007/s00021-024-00875-2","url":null,"abstract":"<div><p>We consider the initial-boundary-value problem of the isentropic compressible Navier–Stokes–Poisson equations subject to large and non-flat doping profile in 3D bounded domain with slip boundary condition and vacuum. The global well-posedness of classical solution is established with small initial energy but possibly large oscillations and vacuum. The steady state (except velocity) and the doping profile are allowed to be of large variation.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140836157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Interactions of Flocking Particles with the Stokes Flow in an Infinite Channel 论成群粒子与无限通道中斯托克斯流的相互作用
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-05-01 DOI: 10.1007/s00021-024-00876-1
Dongnam Ko, Hyeong-Ohk Bae, Seung-Yeal Ha, Gyuyoung Hwang
{"title":"On the Interactions of Flocking Particles with the Stokes Flow in an Infinite Channel","authors":"Dongnam Ko,&nbsp;Hyeong-Ohk Bae,&nbsp;Seung-Yeal Ha,&nbsp;Gyuyoung Hwang","doi":"10.1007/s00021-024-00876-1","DOIUrl":"10.1007/s00021-024-00876-1","url":null,"abstract":"<div><p>We present the global existence of weak solutions to the Cucker–Smale–Stokes system in an infinitely long cylindrical domain with the specular boundary condition. The proposed system consists of the kinetic Cucker–Smale model and the Stokes system for flocking particles and an incompressible fluid, respectively, in an infinitely long cylindrical domain. It models the collective dynamics resulting from the fluid-particle-structure interactions. For this model, we provide the global existence of a weak solution and numerical simulations that exhibit collective behaviors of flocking particles.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of the Restricted ((N+1))-Vortex Problem with a Regular Polygon Distribution 具有规则多边形分布的受限 $$(N+1)$$ - 漩涡问题的动力学原理
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-29 DOI: 10.1007/s00021-024-00866-3
Qihuai Liu, Qian Luo, Chao Wang
{"title":"Dynamics of the Restricted ((N+1))-Vortex Problem with a Regular Polygon Distribution","authors":"Qihuai Liu,&nbsp;Qian Luo,&nbsp;Chao Wang","doi":"10.1007/s00021-024-00866-3","DOIUrl":"10.1007/s00021-024-00866-3","url":null,"abstract":"<div><p>The restricted <span>((N+1))</span>-vortex problem is investigated in the plane with the first <i>N</i> identical vortices forming a relative equilibrium configuration of a regular <i>N</i>-polygon and the vorticity of the last vortex being zero. We characterize the global dynamics using the method of qualitative theory. It can be shown that the equilibrium points of the system are located at the vertices of three different regular <i>N</i>-polygons and the origin. The equilibrium points on one regular polygon are stable, whereas those on the other two regular polygons are unstable. The origin and singularities are also stable and surrounded by dense periodic orbits. For <span>(N=3)</span> or 4, there exist homoclinic and heteroclinic orbits; while for <span>(Nge 5)</span>, the system’s orbits consist of equilibrium points, heteroclinic orbits, and periodic orbits. We numerically study the trajectories of the passive tracer (a particle with zero vorticity) under specific circumstances, which support our theoretical results.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140835594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analysis of a Sturm–Liouville Problem Arising in Atmosphere 大气中出现的 Sturm-Liouville 问题分析
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-26 DOI: 10.1007/s00021-024-00873-4
Kateryna Marynets
{"title":"Analysis of a Sturm–Liouville Problem Arising in Atmosphere","authors":"Kateryna Marynets","doi":"10.1007/s00021-024-00873-4","DOIUrl":"10.1007/s00021-024-00873-4","url":null,"abstract":"<div><p>We present recent results in study of a mathematical model of the sea-breeze flow, arising from a general model of the ’morning glory’ phenomena. Based on analysis of the Dirichlet spectrum of the corresponding Sturm–Liouville problem and application of the Fredholm alternative, we establish conditions of existence/uniqueness of solutions to the given problem.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00021-024-00873-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Well-Posedness and Decay Rates of Solutions to the Poisson–Nernst–Planck–Navier–Stokes System 论泊松-恩斯特-普朗克-纳维尔-斯托克斯系统解的良好拟合和衰减率
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-25 DOI: 10.1007/s00021-024-00867-2
Xiaoping Zhai, Zhigang Wu
{"title":"On the Well-Posedness and Decay Rates of Solutions to the Poisson–Nernst–Planck–Navier–Stokes System","authors":"Xiaoping Zhai,&nbsp;Zhigang Wu","doi":"10.1007/s00021-024-00867-2","DOIUrl":"10.1007/s00021-024-00867-2","url":null,"abstract":"<div><p>We consider the initial value problem associated to the Poisson–Nernst–Planck–Navier–Stokes system which is first derived by Wang et al. (J Differ Equ 262:68–115, 2017) through an Energetic Variational Approach (EVA). Exploiting harmonic analysis tools (especially Littlewood–Paley theory), we first study the local and global well-posedness of the system in critical Besov spaces. Then, under a suitable condition involving only low-frequency of initial data, we use the Lyapunov-type inequality of the energy functionals to establish optimal time decay rates for the constructed global solutions. The proof crucially depends on a careful analysis for treating the extra effect of the distribution for the negative (positive) charge and non-standard product estimates, interpolation inequalities.\u0000</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140655598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ill-Posedness of the Novikov Equation in the Critical Besov Space (B^{1}_{infty ,1}(mathbb {R})) 诺维科夫方程在临界贝索夫空间 $$B^{1}_{infty ,1}(mathbb {R})$$ 中的难解性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-23 DOI: 10.1007/s00021-024-00874-3
Jinlu Li, Yanghai Yu, Weipeng Zhu
{"title":"Ill-Posedness of the Novikov Equation in the Critical Besov Space (B^{1}_{infty ,1}(mathbb {R}))","authors":"Jinlu Li,&nbsp;Yanghai Yu,&nbsp;Weipeng Zhu","doi":"10.1007/s00021-024-00874-3","DOIUrl":"10.1007/s00021-024-00874-3","url":null,"abstract":"<div><p>It is shown that both the Camassa–Holm and Novikov equations are ill-posed in <span>(B_{p,r}^{1+1/p}(mathbb {R}))</span> with <span>((p,r)in [1,infty ]times (1,infty ])</span> in Guo et al. (J Differ Equ 266:1698–1707, 2019) and well-posed in <span>(B_{p,1}^{1+1/p}(mathbb {R}))</span> with <span>(pin [1,infty ))</span> in Ye et al. (J Differ Equ 367: 729–748, 2023). Recently, the ill-posedness for the Camassa–Holm equation in <span>(B^{1}_{infty ,1}(mathbb {R}))</span> has been proved in Guo et al. (J Differ Equ 327: 127–144, 2022). In this paper, we shall solve the only left an endpoint case <span>(r=1)</span> for the Novikov equation. More precisely, we prove the ill-posedness for the Novikov equation in <span>(B^{1}_{infty ,1}(mathbb {R}))</span> by exhibiting the norm inflation phenomena.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability for the Magnetic Bénard System with Partial Dissipation 具有部分耗散的贝纳德磁性系统的稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-17 DOI: 10.1007/s00021-024-00872-5
Yuzhu Wang, Yuhang Zhang, Xiaoping Zhai
{"title":"Stability for the Magnetic Bénard System with Partial Dissipation","authors":"Yuzhu Wang,&nbsp;Yuhang Zhang,&nbsp;Xiaoping Zhai","doi":"10.1007/s00021-024-00872-5","DOIUrl":"10.1007/s00021-024-00872-5","url":null,"abstract":"<div><p>In this paper, we prove the global existence and stability of the magnetic Bénard system with partial dissipation on perturbations near a background magnetic field in <span>({mathbb {T}}^d (d=2,3))</span>. If there is no velocity dissipation, the stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit large-time decay rate of the solutions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation of a Solution to the Stationary Navier–Stokes Equations in a Curved Thin Domain by a Solution to Thin-Film Limit Equations 用薄膜极限方程解法近似曲线薄域中的静态纳维-斯托克斯方程解法
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-15 DOI: 10.1007/s00021-024-00870-7
Tatsu-Hiko Miura
{"title":"Approximation of a Solution to the Stationary Navier–Stokes Equations in a Curved Thin Domain by a Solution to Thin-Film Limit Equations","authors":"Tatsu-Hiko Miura","doi":"10.1007/s00021-024-00870-7","DOIUrl":"10.1007/s00021-024-00870-7","url":null,"abstract":"<div><p>We consider the stationary Navier–Stokes equations in a three-dimensional curved thin domain around a given closed surface under the slip boundary conditions. Our aim is to show that a solution to the bulk equations is approximated by a solution to limit equations on the surface appearing in the thin-film limit of the bulk equations. To this end, we take the average of the bulk solution in the thin direction and estimate the difference of the averaged bulk solution and the surface solution. Then we combine an obtained difference estimate on the surface with an estimate for the difference of the bulk solution and its average to get a difference estimate for the bulk and surface solutions in the thin domain, which shows that the bulk solution is approximated by the surface one when the thickness of the thin domain is sufficiently small.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140573027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Steadiness of Symmetric Solutions to Two Dimensional Dispersive Models 论二维分散模型对称解的稳定性
IF 1.2 3区 数学
Journal of Mathematical Fluid Mechanics Pub Date : 2024-04-15 DOI: 10.1007/s00021-024-00869-0
Long Pei, Fengyang Xiao, Pan Zhang
{"title":"On the Steadiness of Symmetric Solutions to Two Dimensional Dispersive Models","authors":"Long Pei,&nbsp;Fengyang Xiao,&nbsp;Pan Zhang","doi":"10.1007/s00021-024-00869-0","DOIUrl":"10.1007/s00021-024-00869-0","url":null,"abstract":"<div><p>In this paper, we consider the steadiness of symmetric solutions to two dispersive models in shallow water and hyperelastic mechanics, respectively. These models are derived previously in the two-dimensional setting and can be viewed as the generalization of the Camassa–Holm and Kadomtsev–Petviashvili equations. For these two models, we prove that the symmetry of classical solutions implies steadiness in the horizontal direction. We also confirm the connection between symmetry and steadiness for solutions in weak formulation, which covers in particular the peaked solutions.</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140572930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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