In this paper,we propose and analyze a first-order,semi-implicit,and unconditionally energy-stable scheme for an incompressible ferrohydrodynamics flow.We consider the constitutive equation describing the behavior of ...In this paper,we propose and analyze a first-order,semi-implicit,and unconditionally energy-stable scheme for an incompressible ferrohydrodynamics flow.We consider the constitutive equation describing the behavior of magnetic fluid provided by Shliomis,which consists of the Navier-Stokes equation,the magnetization equation,and the magnetostatics equation.By using an existing regularization method,we derive some prior estimates for the solutions.We then bring up a rigorous error analysis of the temporal semi-discretization scheme based on these prior estimates.Through a series of experiments,we verify the convergence and energy stability of the proposed scheme and simulate the behavior of ferrohydrodynamics flow in the background of practical applications.展开更多
In this paper,we propose a fully discrete finite element method for an incompressible ferrohydrodynamics flow.The constitutive equation we consider,proposed by Rosensweig(2002),models the motion of a magnetic fluid.We...In this paper,we propose a fully discrete finite element method for an incompressible ferrohydrodynamics flow.The constitutive equation we consider,proposed by Rosensweig(2002),models the motion of a magnetic fluid.We develop a semi-implicit,energy-stable scheme to solve this nonlinear system.Using the Leray-Schauder fixed point theorem,we establish the existence and uniqueness of the numerical solutions.Additionally,we prove the unconditional convergence of the numerical scheme through the Aubin-Lions-Simon lemma.Numerical experiments are conducted to verify the convergence of our scheme and to simulate the behavior of ferrohydrodynamic flows.展开更多
We analyzed the phenomenon of ferrofiuid magnetoviscosity in high-permeability wall-region non-magnetic porous media of the Müller kind. After upscaling the pore-level ferrohydrodynamic model, we obtained a simpl...We analyzed the phenomenon of ferrofiuid magnetoviscosity in high-permeability wall-region non-magnetic porous media of the Müller kind. After upscaling the pore-level ferrohydrodynamic model, we obtained a simplified volume-average zero-order axisymmetric model for non-Darcy non-turbulent flow of steady-state isothermal incompressible Newtonian ferrofluids through a porous medium experiencing external constant bulk-flow oriented gradient magnetic field, ferrofluid self-consistent demagnetizing field and induced magnetic field in the solid. The model was explored in contexts plagued by wall flow maldistribution due to low column-to-particle diameter ratios. It was shown that for proper magnetic field arrangement, wall channeling can be reduced by inflating wall flow resistance through magnetovisco-thickening and Kelvin body force density which reroute a fraction of wall flow towards bed core. 展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12071404,11971410,12026254)by the Young Elite Scientist Sponsorship Program by CAST(Grant No.2020QNRC001)+1 种基金by the Key Project of Scientific Research Project of Hunan Provincial Department of Education(Grant No.22A0136)by the Postgraduate Scientific Research Innovation Project of Hunan Province(Grant No.CX20210612).
文摘In this paper,we propose and analyze a first-order,semi-implicit,and unconditionally energy-stable scheme for an incompressible ferrohydrodynamics flow.We consider the constitutive equation describing the behavior of magnetic fluid provided by Shliomis,which consists of the Navier-Stokes equation,the magnetization equation,and the magnetostatics equation.By using an existing regularization method,we derive some prior estimates for the solutions.We then bring up a rigorous error analysis of the temporal semi-discretization scheme based on these prior estimates.Through a series of experiments,we verify the convergence and energy stability of the proposed scheme and simulate the behavior of ferrohydrodynamics flow in the background of practical applications.
基金supported by National Natural Science Foundation of China(Grant Nos.12071404,11971410,12071402,and 12261131501)Science and Technology Innovation Program of Hunan Province(Grant No.2024RC3158)+3 种基金Young Elite Scientist Sponsorship Program by China Association for Science and Technology(Grant No.2020QNRC001)Key Project of Scientific Research Project of Hunan Provincial Department of Education(Grant No.22A0136)Project of Scientific Research Fund of the Hunan Provincial Science and Technology Department(Grant Nos.2023GK2029 and 2024ZL5017)Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province of China.
文摘In this paper,we propose a fully discrete finite element method for an incompressible ferrohydrodynamics flow.The constitutive equation we consider,proposed by Rosensweig(2002),models the motion of a magnetic fluid.We develop a semi-implicit,energy-stable scheme to solve this nonlinear system.Using the Leray-Schauder fixed point theorem,we establish the existence and uniqueness of the numerical solutions.Additionally,we prove the unconditional convergence of the numerical scheme through the Aubin-Lions-Simon lemma.Numerical experiments are conducted to verify the convergence of our scheme and to simulate the behavior of ferrohydrodynamic flows.
文摘We analyzed the phenomenon of ferrofiuid magnetoviscosity in high-permeability wall-region non-magnetic porous media of the Müller kind. After upscaling the pore-level ferrohydrodynamic model, we obtained a simplified volume-average zero-order axisymmetric model for non-Darcy non-turbulent flow of steady-state isothermal incompressible Newtonian ferrofluids through a porous medium experiencing external constant bulk-flow oriented gradient magnetic field, ferrofluid self-consistent demagnetizing field and induced magnetic field in the solid. The model was explored in contexts plagued by wall flow maldistribution due to low column-to-particle diameter ratios. It was shown that for proper magnetic field arrangement, wall channeling can be reduced by inflating wall flow resistance through magnetovisco-thickening and Kelvin body force density which reroute a fraction of wall flow towards bed core.
