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A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is proposed and applied to accurately compute steady and unsteady incompressible flows. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth-order compact FD scheme, and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to stabilize the numerical solution. An iterative initialization procedure is presented and applied to generate consistent initial conditions for the simulation of unsteady flows. A sensitivity study is also... 

A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is extended and applied to accurately simulate two-phase liquid-vapor flows with high density ratios. Herein, the He-Shan-Doolen-type lattice Boltzmann multiphase model is used and the spatial derivatives in the resulting equations are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient two-phase flow solver. A high-order spectral-type low-pass compact nonlinear filter is used to regularize the numerical solution and remove spurious waves generated by flow nonlinearities in smooth regions... 

In this study, the Chebyshev collocation spectral lattice Boltzmann method (CCSLBM) is developed and assessed for the computation of low-speed flows. Both steady and unsteady flows are considered here. The discrete Boltzmann equation with the Bhatnagar-Gross-Krook approximation based on the pressure distribution function is considered and the space discretization is performed by the Chebyshev collocation spectral method to achieve a highly accurate flow solver. To provide accurate unsteady solutions, the time integration of the temporal term in the lattice Boltzmann equation is made by the fourth-order Runge-Kutta scheme. To achieve numerical stability and accuracy, physical boundary... 

This paper investigates numerically the problem of unsteady magnetohydrodynamic nanofluid flow and heat transfer between parallel plates due to the normal motion of the porous upper plate. The governing equations are solved via the fourth-order Runge-Kutta method. Different kind of nanoparticles is examined. The effects of kind of nanoparticle, nanofluid volume fraction, expansion ratio, Hartmann number, Reynolds number on velocity and temperature profiles are considered. Also effect of different types of nanoparticles is examined. Results indicate that velocity decreases with increase of Hartmann number due to effect of Lorentz forces. Rate of heat transfer increase with increase of... 

In this study, the numerical simulation of the fluid flow and acoustic field of a supersonic jet is performed by using high-order discretization and the vorticity confinement (VC) method on coarse grids. The three-dimensional Navier-Stokes equations are considered in the generalized curvilinear coordinate system and the high-order compact finite-difference scheme is applied for the space discretization, and the time integration is performed by the fourth-order Runge-Kutta scheme. A low-pass high-order filter is applied to stabilize the numerical solution. The non-reflecting boundary conditions are adopted for all the free boundaries, and the Kirchhoff surface integration is utilized to... 

As the most rigid cytoskeletal filaments, tubulin–labeled microtubules bear compressive forces in living cells, balancing the tensile forces within the cytoskeleton to maintain the cell shape. The current structure is often under several environmental conditions as well as various dynamic or static loads that can decrease the stability of the viscoelastic tubulin–labeled microtubules. For this issue, the dynamic stability analysis of size-dependent viscoelastic tubulin–labeled microtubules using modified strain gradient theory by considering the exact three-length scale parameter. Viscoelastic properties are modeled using Kelvin-Voight model to study the time-dependent tubulin–labeled...