A new approach to the solution of the Navier-Stokes equations

1987 ◽  
Vol 7 (12) ◽  
pp. 1315-1324 ◽  
Author(s):  
George W. Grossman ◽  
Ronald M. Barron
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
New Approach

Lattice Boltzmann Method for the Simulating Extrudate Swell of Viscoelastic Fluid

2015 ◽  
Vol 799-800 ◽  
pp. 784-787
Author(s):  
Wen Qin Liu ◽  
Yong Li
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Extrudate Swell ◽  
Navier Stokes Equations ◽  
New Approach ◽  
Moving Interface ◽  
Good Accord ◽  
Boltzmann Method

The main objective of this work is to develop a new approach based on the Lattice Boltzmann method (LBM) to simulate the extrudate swell of an Oldroyd B viscoelatic fluid. Two lattice Boltzmann equations are used to solve the Navier-Stokes equations and constitutive equation simultaneously at each time iteration. The single LBM model is used to track the moving interface in this paper. To validate the accuracy and stability of this new scheme, we study the steady 2D Poiseuille flow firstly, finding the numerical results be in good accord with the analytical solution. Then the die-swell phenomenon is solved, we successfully acquire the different swelling state of an Oldroyd B fluid at different time.

A New Scaling for Tornado-Like Vortices

2005 ◽  
Vol 62 (7) ◽  
pp. 2639-2645 ◽  
Author(s):  
David S. Nolan
Keyword(s):  
Numerical Simulations ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
New Approach ◽  
Physical Reasoning

Abstract A new approach is presented for the nondimensionalization of the Navier–Stokes equations for tornado-like vortices. This scaling is based on the results of recent numerical simulations and physical reasoning. The method clarifies and unifies the results of numerous earlier studies that used numerical simulations of axisymmetric incompressible flow to study tornadoes. Some examples are presented.

scholarly journals A new approach for solving compressible Navier-Stokes equations

2017 ◽  
Vol 4 (12) ◽  
pp. 133-144
Author(s):  
A. S. J. Al-Saif ◽  
◽  
Takia Ahmed J. Al-Griffi ◽  
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
New Approach

On a New Approach to Slip Flow Using Rayleigh’s Problem

1967 ◽  
Vol 34 (4) ◽  
pp. 837-839 ◽  
Author(s):  
E. P. Russo ◽  
O. A. Arnas
Keyword(s):  
Boundary Condition ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Slip Velocity ◽  
Stokes Equations ◽  
Traditional Approach ◽  
Slip Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
New Approach

A new approach, involving a perturbation of the Navier-Stokes equations, is used to analyze the phenomenon of slip flow over a flat plate. An expression for the coefficient of drag is derived and compared to the drag coefficient obtained by the traditional approach of solving the Navier-Stokes equations with a slip-velocity boundary condition.

Performance of r-Adaptation Using Truncation Error-Based Equidistribution

2019 ◽  
Vol 4 (4) ◽  
Author(s):  
Charles W. Jackson ◽  
Christopher J. Roy
Keyword(s):  
Truncation Error ◽  
Stokes Equations ◽  
Computational Cost ◽  
Discretization Error ◽  
New Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Error Level ◽  
Navier Stokes Equations ◽  
New Approach

Abstract This paper investigates the computational cost of performing r-adaptation by equidistributing the truncation error. This adaptation approach is applied to several two-dimensional (2D) problems using the Euler and laminar Navier–Stokes equations. The costs of performing the adaptation are compared to uniform refinement, and it is shown that adaptation can be far cheaper than uniform refinement. This paper also presents a new method of refining the equidistributed meshes. This new approach allows the adaptation to be performed on much coarser meshes and provides a method of refining these coarse, adapted meshes to meet a discretization-error target for the problem. We show that this approach can be at least 16–24 times cheaper than uniform refinement for the problems investigated here. This approach also is at least ten times faster than performing r-adaptation on a fine enough mesh to obtain the target discretization-error level.

scholarly journals Implementing Boundary Conditions in Simulations of Arterial Flows

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
P. Bokov ◽  
P. Flaud ◽  
A. Bensalah ◽  
J.-M. Fullana ◽  
M. Rossi
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Interaction Model ◽  
Navier Stokes ◽  
Reflection Index ◽  
Navier Stokes Equations ◽  
New Approach ◽  
Classical Boundary ◽  
Artery First ◽  
Nonreflecting Boundary Condition

Computational hemodynamic models of the cardiovascular system are often limited to finite segments of the system and therefore need well-controlled inlet and outlet boundary conditions. Classical boundary conditions are measured total pressure or flow rate imposed at the inlet and impedances of RLR, RLC, or LR filters at the outlet. We present a new approach based on an unidirectional propagative approach (UPA) to model the inlet/outlet boundary conditions on the axisymmetric Navier–Stokes equations. This condition is equivalent to a nonreflecting boundary condition in a fluid–structure interaction model of an axisymmetric artery. First we compare the UPA to the best impedance filter (RLC). Second, we apply this approach to a physiological situation, i.e., the presence of a stented segment into a coronary artery. In that case a reflection index is defined which quantifies the amount of pressure waves reflected upon the singularity.

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