scholarly journals Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 233
Author(s):  
Galina Muratova ◽  
Tatiana Martynova ◽  
Evgeniya Andreeva ◽  
Vadim Bavin ◽  
Zeng-Qi Wang
Keyword(s):  
Stokes Equations ◽  
Hermitian Matrix ◽  
Multigrid Methods ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Algebraic Equations ◽  
Navier Stokes Equations ◽  
Linear Algebraic Equations ◽  
Discretized Systems

Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier–Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented.

scholarly journals Detection of multiple solutions using a mid-cell back substitution technique applied to computational fluid dynamics

2000 ◽  
Vol 214 (11) ◽  
pp. 1401-1407
Author(s):  
S R Kendall ◽  
H V Rao
Keyword(s):  
Multiple Solutions ◽  
Computational Models ◽  
Stokes Equations ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Algebraic Equations ◽  
Navier Stokes Equations ◽  
Flow Modelling ◽  
Spurious Solutions ◽  
Linear Algebraic Equations

Computational models for fluid flow based on the Navier-Stokes equations for compressible fluids led to numerical procedures requiring the solution of simultaneous non-linear algebraic equations. These give rise to the possibility of multiple solutions, and hence there is a need to monitor convergence towards a physically meaningful flow field. The number of possible solutions that may arise is examined, and a mid-cell back substitution technique (MCBST) is developed to detect and avoid convergence towards apparently spurious solutions. The MCBST was used successfully for flow modelling in micron-sized flow passages, and was found to be particularly useful in the early stages of computation, optimizing the speed of convergence.

SCALING OF FLUID RECOVERY FROM PERCOLATION FRACTALS

Fractals ◽  
1994 ◽  
Vol 02 (02) ◽  
pp. 269-272 ◽  
Author(s):  
IAN D WEDGWOOD ◽  
DONALD M MONRO
Keyword(s):  
Stokes Equations ◽  
Petroleum Reservoirs ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Reservoir Models ◽  
Wide Range

We report on the recovery of fluid driven through percolation lattices across a range of scales using a finite difference approximation to the Navier-Stokes equation. This is important in the study of recovery from petroleum reservoirs, in which flow occurs over a wide range of scales, from the microscopic pores right up to the full reservoir. This variation of scale presents difficulties, since flow at the pore level is subject to predominantly viscous effects, whereas at the larger scales the viscous effects may become negligible in comparison with inertial effects. The Navier-Stokes equations may differ greatly with scale. Theoretical rock structures are created using percolation lattices and the flow properties of identical rock structures are then examined as a function of scale. The resultant recovery rates exhibit similarity across scale which would simplify the study of geological reservoir models.

scholarly journals Numerical simulation of the flow of viscous incompressible fluid through cylindrical cavities

2019 ◽  
pp. 218-221
Author(s):  
Ya. P. Trotsenko
Keyword(s):  
Incompressible Fluid ◽  
Shear Layer ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Oscillation Mode ◽  
Navier Stokes ◽  
Sustained Oscillation ◽  
Tvd Scheme ◽  
Algebraic Equations ◽  
Linear Algebraic Equations

The flow of viscous incompressible fluid in a cylindrical duct with two serial diaphragms is studied by the numerical solution of the unsteady Navier–Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is nonstationary and is characterized by the presence of an unstable shear layer under certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity and pressure fields in the orifice of the second diaphragm. There can be four self-sustained oscillation modes depending on the length of the cavity formed by the diaphragms. With the increase in the distance between the diaphragms, the frequency of oscillations decreases within the same self-oscillation mode and rises sharply with the switch to the next mode.

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