scholarly journals Axisymmetric Slow Motion of a Porous Spherical Particle in a Viscous Fluid Using Time Fractional Navier–Stokes Equation

2021 ◽  
Vol 5 (2) ◽  
pp. 24
Author(s):  
Jai Prakash ◽  
Chirala Satyanarayana
Keyword(s):  
Viscous Fluid ◽  
Spherical Particle ◽  
Stokes Equation ◽  
Fractional Order ◽  
Drag Force ◽  
Translational Motion ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Laplace Transform Technique

In this paper, we present the unsteady translational motion of a porous spherical particle in an incompressible viscous fluid. In this case, the modified Navier–Stokes equation with fractional order time derivative is used for conservation of momentum external to the particle whereas modified Brinkman equation with fractional order time derivative is used internal to the particle to govern the fluid flow. Stress jump condition for the tangential stress along with continuity of normal stress and continuity of velocity vectors is used at the porous–liquid interface. The integral Laplace transform technique is employed to solve the governing equations in fluid and porous regions. Numerical inversion code in MATLAB is used to obtain the solution of the problem in the physical domain. Drag force experienced by the particle is obtained. The numerical results have been discussed with the aid of graphs for some specific flows, namely damping oscillation, sine oscillation and sudden motion. Our result shows a significant contribution of the jump coefficient and the fractional order parameter to the drag force.

Adomian’s Method Applied to Navier-Stokes Equation With a Fractional Order

2009 ◽  
Author(s):  
Yihong Wang ◽  
Zhengang Zhao ◽  
Changpin Li ◽  
YangQuan Chen
Keyword(s):  
Stokes Equation ◽  
Fractional Order ◽  
Analytic Solution ◽  
Navier Stokes ◽  
Approximate Analytic Solution ◽  
Navier Stokes Equation

In this paper, Adomian’s method is effectively implemented to determine the (approximate) analytic solution of the fractional-order Navier-Stokes equation. Such a solution is expressed in the form of a series with easily computable components. An illustrative example is presented.

scholarly journals Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 864 ◽  
Author(s):  
Ana Bela Cruzeiro
Keyword(s):  
Fluid Dynamics ◽  
Variational Principle ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Time Derivative ◽  
Probabilistic Methods ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle.

scholarly journals The complete Solution for existence and smoothness of Navier-Stokes equation

2018 ◽  
Author(s):  
Mihir Kumar Jha
Keyword(s):  
General Solution ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Stokes Equation ◽  
Complete Solution ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Second Law ◽  
Navier Stokes Equation ◽  
Coupled Differential Equations

The motive of this paper is to put forward a general solution to Navier-stokes equation which describes the motion of viscous fluid substances, derived by applying Newton’s second law to fluid motion. These equations are the set of coupled differential equations, which are too difficult to solve analytically.

scholarly journals Space Analyticity and Bounds for Derivatives of Solutions to the Evolutionary Equations of Diffusive Magnetohydrodynamics

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1789
Author(s):  
Vladislav Zheligovsky
Keyword(s):  
Stokes Equation ◽  
Arbitrary Order ◽  
Numerical Study ◽  
A Priori ◽  
Auxiliary Problem ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Evolutionary Equations ◽  
Derivatives Of

In 1981, Foias, Guillopé and Temam proved a priori estimates for arbitrary-order space derivatives of solutions to the Navier–Stokes equation. Such bounds are instructive in the numerical investigation of intermittency that is often observed in simulations, e.g., numerical study of vorticity moments by Donzis et al. (2013) revealed depletion of nonlinearity that may be responsible for smoothness of solutions to the Navier–Stokes equation. We employ an original method to derive analogous estimates for space derivatives of three-dimensional space-periodic weak solutions to the evolutionary equations of diffusive magnetohydrodynamics. Construction relies on space analyticity of the solutions at almost all times. An auxiliary problem is introduced, and a Sobolev norm of its solutions bounds from below the size in C3 of the region of space analyticity of the solutions to the original problem. We recover the exponents obtained earlier for the hydrodynamic problem. Moreover, the same approach is followed here to derive and prove similar a priori bounds for arbitrary-order space derivatives of the first-order time derivative of the weak MHD solutions.

scholarly journals Analysis of fractional multi-dimensional Navier–Stokes equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yu-Ming Chu ◽  
Nehad Ali Shah ◽  
Praveen Agarwal ◽  
Jae Dong Chung
Keyword(s):  
Stokes Equation ◽  
Fractional Order ◽  
Hybrid Method ◽  
Current Method ◽  
Navier Stokes ◽  
Science And Engineering ◽  
Navier Stokes Equation ◽  
Transform Method ◽  
Variational Iteration ◽  
He’S Polynomials

AbstractIn this paper, a hybrid method called variational iteration transform method has been implemented to solve fractional-order Navier–Stokes equation. Caputo operator describes fractional-order derivatives. The solutions of three examples are presented to show the validity of the current method without using Adomian and He’s polynomials. The results of the proposed method are shown and analyzed with the help of figures. It is shown that the proposed method is found to be efficient, reliable, and easy to implement for various related problems of science and engineering.

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