Numerical solution of the Navier-Stokes equation for flow past spheres: Part I. Viscous flow around spheres with and without radial mass efflux

AIChE Journal ◽  
1967 ◽  
Vol 13 (2) ◽  
pp. 212-219 ◽  
Author(s):  
A. E. Hamielec ◽  
T. W. Hoffman ◽  
L. L. Ross
Keyword(s):  
Numerical Solution ◽  
Viscous Flow ◽  
Stokes Equation ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Flow Past

scholarly journals Numerical solution of Navier stokes equation using control volume and finite element method

2016 ◽  
Vol 5 (1) ◽  
pp. 63
Author(s):  
Musa Adam Aigo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Stokes Equation ◽  
Control Volume ◽  
Navier Stokes ◽  
Weak Formulation ◽  
Navier Stokes Equation ◽  
Fast Solution ◽  
Element Method

<p>The aim of this paper is twofold first we will  provide a numerical solution of the Navier Stokes equation using the Projection technique and finite element method. The problem will be introduced in weak formulation and a Finite Element method will be developed, then solve in a fast way the sparse system derived. Second, the projection method with Control volume approach will be applied to get a fast solution, in iterations count.</p>

An Efficient Technique of Linearization towards Fourth Order Finite Differences for Numerical Solution of the 1D Burgers Equation

2014 ◽  
Vol 348 ◽  
pp. 285-290 ◽  
Author(s):  
M.M. Cruz ◽  
M.D. Campos ◽  
J.A. Martins ◽  
E.C. Romão
Keyword(s):  
Pressure Gradient ◽  
Numerical Solution ◽  
Stokes Equation ◽  
Fourth Order ◽  
Finite Differences ◽  
Burgers Equation ◽  
Efficient Technique ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Linearization Technique

This work aims to solve the 1D Burgers equation, which represents a simplification of the Navier-Stokes equation, supposing the yielding only at x-direction and without pressure gradient. For such a solution, an implicit scheme (Cranck-Nicolson method) with a fourth order precision in space is utilized. The main contribution of this work is the application of a linearization technique of the non-linear term (advective term), and then, towards the analytical and numerical results from literature, validate and demonstrate it as being highly satisfactory.

scholarly journals Vortex sheet turbulence as solvable string theory

2021 ◽  
Vol 36 (05) ◽  
pp. 2150062
Author(s):  
Alexander Migdal
Keyword(s):  
String Theory ◽  
Stokes Equation ◽  
Potential Flow ◽  
Vortex Sheet ◽  
Gibbs Distribution ◽  
Navier Stokes ◽  
Normal Displacement ◽  
Navier Stokes Equation ◽  
Flow Past ◽  
Steady Solutions

We study steady vortex sheet solutions of the Navier–Stokes in the limit of vanishing viscosity at fixed energy flow. We refer to this as the turbulent limit. These steady flows correspond to a minimum of the Euler Hamiltonian as a functional of the tangent discontinuity of the local velocity parametrized as [Formula: see text]. This observation means that the steady flow represents the low-temperature limit of the Gibbs distribution for vortex sheet dynamics with the normal displacement [Formula: see text] of the vortex sheet as a Hamiltonian coordinate and [Formula: see text] as a conjugate momentum. An infinite number of Euler conservation laws lead to a degenerate vacuum of this system, which explains the complexity of turbulence statistics and provides the relevant degrees of freedom (random surfaces). The simplest example of a steady solution of the Navier–Stokes equation in the turbulent limit is a spherical vortex sheet whose flow outside is equivalent to a potential flow past a sphere, while the velocity is constant inside the sphere. Potential flow past other bodies provide other steady solutions. The new ingredient we add is a calculable gap in tangent velocity, leading to anomalous dissipation. This family of steady solutions provides an example of the Euler instanton advocated in our recent work, which is supposed to be responsible for the dissipation of the Navier–Stokes equation in the turbulent limit. We further conclude that one can obtain turbulent statistics from the Gibbs statistics of vortex sheets by adding Lagrange multipliers for the conserved volume inside closed surfaces, the rate of energy pumping, and energy dissipation. The effective temperature in our Gibbs distribution goes to zero as [Formula: see text] with Reynolds number [Formula: see text] in the turbulent limit. The Gibbs statistics in this limit reduces to the solvable string theory in two dimensions (so-called [Formula: see text] critical matrix model). This opens the way for nonperturbative calculations in the Vortex Sheet Turbulence, some of which we report here.

Numerical Solution of Time Fractional Navier-Stokes Equation by Discrete Adomian decomposition method

2014 ◽  
Vol 3 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Gunvant A. Birajdar
Keyword(s):  
Exact Solution ◽  
Numerical Solution ◽  
Stokes Equation ◽  
Decomposition Method ◽  
Graphical Representation ◽  
Adomian Decomposition Method ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Space Domain ◽  
Adomian Decomposition

AbstractIn this paper we find the solution of time fractional discrete Navier-Stokes equation using Adomian decomposition method. Here we discretize the space domain. The graphical representation of solution given by using Matlab software, and it compared with exact solution for alpha = 1.

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