Local Navier-Stokes Equations Research Articles

A Hybrid Analytical Approximate Technique for Solving Two-dimensional Incompressible Flow in Lid-driven Square Cavity Problem

This paper suggests a new technique for finding the analytical approximate solutions to two-dimensional kinetically reduced local Navier-Stokes equations. This new scheme depends combines the q-Homotopy analysis method (q-HAM) , Laplace transform, and Padé approximant method. The power of the new methodology is confirmed by applying it to the flow problem of the lid-driven square cavity. The numerical results obtained by using the proposed method showed that the new technique has good convergence, high accuracy, and efficiency compared with the earlier studies. Moreover, the graphs and tables demonstrate the new approach’s validity.

Optimized finite difference method with artificial dissipation for under-resolved unsteady incompressible flow computations using kinetically reduced local Navier-Stokes equations

Under-resolved unsteady incompressible flow computations employed on coarser grids are presented. Kinetically Reduced Local Navier-Stokes (KRLNS) equations is a newly method to deal with unsteady incompressible flows, which is applicable to the unsteady incompressible flows without the need for sub-iterations and is capable of capturing the correct transient behavior. To stabilize the computations and achieve high accuracy, the KRLNS equations is discretized with higher order standard and optimized types of central finite difference method (FDM) together with artificial dissipation or spatial filter and is integrated by using 4-stage Runge-Kutta method. Numerical simulations of 2D doubly periodic shear layers are carried out on coarser regular grids and the computed solutions are compared with those obtained on finer grids. The parallel computations are implemented on multiple GPU (Tesla K40) system with 4 GPUs, based on the domain decomposition method and the acceleration is investigated. It is found that the solution obtained by optimized type of FDM is more accurate than that of standard one especially for much coarser grids, and that the proposed approach is easy to perform the parallel computations and obtain a large acceleration according to the number of GPUs used.

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.

Computation of Unsteady Incompressible Viscous Flows Using Kinetically Reduced Local Navier-Stokes Equations on a GPU

Kinetically Reduced Local Navier-Stokes (KRLNS) equations are applied for two-dimensional (2-D) simulations of Womersley problem and doubly periodic shear layers in order to demonstrate the accuracy, efficiency and the capability to capture the correct transient behavior. The numerical results obtained by the KRLNS equations are compared with those obtained by the pseudo-spectral method (PSM), which is a standard approach to incompressible viscous flows for low Mach number, as well as Lattice Boltzmann Method (LBM). It is confirmed that the KRLNS method can capture the correct transient behavior without use of sub-iterations due to a smoothing effect introduced by using the Grand potential in the continuity equation, and keep the fluctuation of velocity divergence at smaller level by giving an appropriately low Mach number. Parallel computation is carried out on a GPU based on NVIDIA Tesla C1060 system and the provided CUDA library.

G010021 非圧縮性局所ナビエ・ストークス方程式と仮想流束法を用いた流路内流れの数値計算

G010021 非圧縮性局所ナビエ・ストークス方程式と仮想流束法を用いた流路内流れの数値計算

RHEOLOGY OF SUSPENSIONS OF MASS-POLARIZED PARTICLES IN A GRAVITATIONAL FIELD

We derive the complete set of equations of motion for a suspension of mass-polarized rigid particles in a gravity field. The particles are acted upon by forces and couples exerted by the surrounding fluid and by the external gravity field. Besides their mass, momentum, and energy, the particles are characterized by their angular momentum and their (mass) polarization. We discuss the many cross-effects that involve their translational and angular velocities. The balance equations for the fluid phase are obtained from the ensemble average of the local Navier-Stokes equations, while the equations of motion for the particulate phase are obtained by ensemble-averaging the equations for a single particle, much like that in the kinetic theory of gases. We explain why this approach leads to a nonsymmetric stress tensor for the whole suspension, in contrast with the two-fluid approach in which the suspension stress tensor is perfectly symmetric for a suspension of this kind.

Kinetically reduced local Navier-Stokes equations for simulation of incompressible viscous flows

Recently, another approach to study incompressible fluid flow was suggested [S. Ansumali, I. Karlin, and H. Ottinger, Phys. Rev. Lett. 94, 080602 (2005)]-the kinetically reduced local Navier-Stokes (KRLNS) equations. We consider a simplified two-dimensional KRLNS system and compare it with Chorin's artificial compressibility method. A comparison of the two methods for steady state computation of the flow in a lid-driven cavity at various Reynolds numbers shows that the results from both methods are in good agreement with each other. However, in the transient flow, it is demonstrated that the KRLNS equations correctly describe the time evolution of the velocity and of the pressure, unlike the artificial compressibility method.

Kinetically reduced local Navier-Stokes equations: An alternative approach to hydrodynamics

An alternative approach, the kinetically reduced local Navier-Stokes (KRLNS) equations for the grand potential and the momentum, is proposed for the simulation of low Mach number flows. The Taylor-Green vortex flow is considered in the KRLNS framework, and compared to the results of the direct numerical simulation of the incompressible Navier-Stokes equations. The excellent agreement between the KRLNS equations and the incompressible nonlocal Navier-Stokes equations for this nontrivial time-dependent flow indicates that the former is a viable alternative for computational fluid dynamics at low Mach numbers.