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A new boundary condition is developed to enhance numerical stability for moving walls in lattice-Boltzmann simulations. It includes a population "adjustment" procedure at boundaries which allows stable simulations closer to the theoretical limit of τ = 0.5. Couette and lid-driven cavity flow simulations show improved velocity profiles, lower stable relaxation timestep τ and higher Reynolds number Re limits. The new method needs fewer timesteps to achieve steady-state.

In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB(N;Q_x,Q_y,Q_z) family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is the SLB(N;K,L,M) family, derived by using the spherical coordinate system and the Gauss–Laguerre, as well as the Gauss–Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.

The Gauss–Laguerre quadrature method is used to construct three-dimensional thermal Lattice Boltzmann models that exactly recover integrals of the equilibrium distribution function over Cartesian octants of the momentum space. We illustrate the capability of these models to exactly implement the diffuse reflection boundary conditions by considering the Couette flow at various values of the Knudsen number.

The unsteady flow in an annulus due to a velocity applied to one of the boundaries is addressed. The fluid considered is non-Newtonian, incompressible and electrically conducting. The strength of the applied magnetic field is time-dependent. Both analytical and numerical approaches are presented and compared. The nonlinear effects on the velocity profile are shown.

This study presents an investigation on the generalized Couette flow of two immiscible Newtonian fluids in an anisotropic porous medium. The flow occurs between two parallel plates, driven by the combined effects of an axial pressure gradient and the movement of the upper plate. The region between the plates is filled with an anisotropic porous medium characterized by directional permeability. An exact solution is derived for the proposed problem by considering appropriate boundary and interface conditions. The slip condition is employed at the lower plate of the channel which has a significant role in the flow mechanics of fluids flowing through porous medium. The effects of directional permeability on the flow of immiscible fluids are explored, and specific cases are presented. This study reveals a significant influence of directional permeability on the flow velocity of both fluids. Furthermore, quantitative conclusions are drawn regarding the shear stress at the lower and upper wall of the channel, with implications for the anisotropic nature of blood arteries. The findings contribute to a deeper understanding of fluid flow in anisotropic porous media and have potential applications in various engineering domains.

The solution of the field equations of the cylindrical Couette flow problem for a rarefied gas is found when the state of equilibrium between the cylinders is perturbed by the following small thermodynamic forces: (i) a pressure difference; (ii) an angular velocity difference; and (iii) a temperature difference. The flow is analyzed within the framework of continuum mechanics by using the field equations that follow from the balance equations of mass, momentum and energy of a viscous and heat conducting gas. These equations are solved analytically by considering slip and jump boundary conditions. The fields of density, velocity, temperature, heat flux vector and viscous stress tensor are calculated as functions of the Knudsen number and of the angular velocity of the rotating cylinders for each thermodynamic force. The asymptotic behaviors of these fields are compared with those obtained from a kinetic model of the Boltzmann equation. The influence of the slip and jump boundary conditions on the solutions is also discussed.

We study mathematically a system of partial differential equations arising in the modeling of an aging fluid, a particular class of non-Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behavior of the solutions.

In this paper, we consider the stability of three-dimensional compressible viscous fluid around the plane Couette flow in the presence of a uniform transverse magnetic field and show that the uniform transverse magnetic field has a stabilizing effect on the plane Couette flow. Namely, for a sufficiently large Hartmann number, the compressible viscous plane Couette flow is nonlinear stable for small Mach number and arbitrary Reynolds number so long as the initial perturbation is small enough.

Smoothed particle hydrodynamics (SPH), dissipative particle dynamics (DPD) and smoothed dissipative particle dynamics (SDPD) are three typical and related particle-based methods. They have been increasingly attractive for solving fluid flow problems, especially for the biofluid flow, because of their advantages of ease and flexibility in modeling complex structure fluids. This work aims to review what the exact similarities and differences are among them, by studying four simple fluid flows: (i) self-diffusion of quiescent flow, (ii) time-dependent Coutte flow, (iii) time-dependent Poiseuille flow, and (iv) lid-driven cavity flow. The simulations show that SPH, DPD and SDPD can give the similar results. SPH generates quite smooth results and has zero system temperature due to the absence of thermal fluctuations, suitable for macroscale problems. However, DPD and SDPD have fluctuating results around the reference results and nonzero system temperature with considerable thermal fluctuations, suitable for mesoscale problems. SDPD is more convenient than DPD to some extent, because it is not required to pre-define the force coefficients. SDPD can adopt more diverse equation of state (EOS) than DPD, because its EOS is user-defined unlike the EOS of DPD, inbuilt in the formulations.

Some Couette flows of a Maxwell fluid caused by the bottom plate applying shear rate on the fluid, are studied. Exact expressions for velocity and shear stress corresponding to the fluid motion are determined using Laplace transform. Two particular cases of constant shear rate on the bottom plate and sinusoidal oscillations of the wall shear rate are discussed. Some important characteristics of fluid motion are highlighted through graphs.

In this paper, an improved dissipative particle dynamics (DPD) model is proposed to simulate magnetorheological (MR) suspension by using the cubic spline function to represent the interactions between magnetic and fluid particles. The model’s accuracy has been verified and validated through carrying out a number of simulations on simple fluids and MR fluids, in which both qualitative and quantitative agreements are observed between the DPD simulation results and the experimental findings and theoretical models in the existing literature. A series of numerical experiments are then conducted on MR fluids, thereby the microstructure evolution and flow properties of MR fluids in Couette and Poiseuille flows are investigated and the effects of some critical factors are particularly explored. Simulation results reveal that the plug region size, which relates to the yield stress of MR fluids, shows an increasing trend with the increase of magnetic field strength, particle volume fraction, particle mass but a decreasing trend with the increase of Mason number and pressure gradient; however, it remains almost unchanged with varying temperature.