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UNCONDITIONAL CONVERGENCE AND ERROR ESTIMATES OF A FULLY DISCRETE FINITE ELEMENT METHOD FOR THE micropolar NAVIER-STOKES EQUATIONS

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Journal of Computational Mathematics 2024年第1期42卷 71-110页

作者： Shipeng Mao Jiaao Sun Wendong Xue NCMIS LSECInstitute of Computational Mathematics and Scientific/Enginnering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element *** first establish some regularity results for the solution of MNSE,which seem to be not available in the ***,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete ***,certain regularity results for the time discrete solution are establishes *** on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of ***,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.

关键词： micropolar fluids Regularity estimates Euler semi-implicit scheme Mixed finite element methods Unconditional convergence

Boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretching vertical surface with prescribed skin friction

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International Journal of Minerals,Metallurgy and Materials 2011年第4期18卷 502-507页

作者： Kartini Ahmad Roslinda Nazar Ioan Pop Centre for Foundation Studies International Islamic University Malaysia46350 Petaling JayaSelangorMalaysia School of Mathematical Sciences Faculty of Science and TechnologyUniversiti Kebangsaan Malaysia43600 UKM BangiSelangorMalaysia Faculty of Mathematics University of ClujR-3400 ClujCP 253Romania

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were *** governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting *** for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to *** assisting（heated plate） and opposing（cooled plate） flow regions are *** is found that dual solutions exist for both assisting and opposing flows.

关键词： boundary layer flow dual solutions micropolar fluids mixed convection skin friction

NONLINEAR STABILITY OF RAREFACTION WAVES FOR A COMPRESSIBLE micropolar FLUID MODEL WITH ZERO HEAT CONDUCTIVITY

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Acta Mathematica Scientia 2020年第5期40卷 1352-1390页

作者：金晶 Noor REHMAN 江芹 School of Mathematics and Statistics Huanggang Normal UniversityHuanggang 438000China School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

In 2018,Duan[1]studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid *** to the absence of heat conductivity,it is quite difficult to close the energy *** considered the far-field states of the initial data to be constants;that is,lim x→±∞(v0,u0,w0,θ0)(x)=(1,0,0,1).He proved that the solution tends asymptotically to those *** this article,under the same hypothesis that the heat conductivity is zero,we consider the far-field states of the initial data to be different constants-that is,lim x→±∞(v0,u0,w0,θ0)(x)=(v±,u±,o,θ±)-and we prove that if both the initial perturbation and the strength of the rarefaction waves are assumed to be suitably small,the Cauchy problem admits a unique global solution that tends time-asymptotically toward the combination of two rarefaction waves from different families.

关键词： micropolar fluids rarefaction wave zero-heat conductivity

MHD stagnation point flow of a micropolar fluid towards a heated surface

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Applied Mathematics and Mechanics(English Edition) 2011年第1期32卷 45-54页

作者： M.ASHRAF M.M.ASHRAF Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University

The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.

关键词： magnetohydrodynamics (MHD) stagnation flow micropolar fluids finitedifferences similarity transformations boundary layer