A Multigrid Flux-Difference Splitting Method for Steady Incompressible Navier-Stokes Equations

1990 ◽  
pp. 99-108 ◽  
Author(s):  
E. Dick ◽  
J. Linden
Keyword(s):  
Stokes Equations ◽  
Splitting Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flux Difference

scholarly journals A finite element dimensional splitting method for 3D rotating Navier-Stokes equations

2015 ◽  
Vol 45 (8) ◽  
pp. 1299-1318
Author(s):  
Wu ZHANG ◽  
HongZhou FAN ◽  
Jian SU ◽  
KaiTai LI ◽  
AiXiang HUANG
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Splitting Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dimensional Splitting

scholarly journals New Splitting Methods for Convection-Dominated Diffusion Problems and Navier-Stokes Equations

2014 ◽  
Vol 16 (5) ◽  
pp. 1239-1262 ◽  
Author(s):  
Feng Shi ◽  
Guoping Liang ◽  
Yubo Zhao ◽  
Jun Zou
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Splitting Method ◽  
Iterative Solvers ◽  
Diffusion System ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Diffusion Problems

AbstractWe present a new splitting method for time-dependent convention-dominated diffusion problems. The original convention diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. A few important features of the scheme lie in the facts that the convection subproblem is solved explicitly and multistep techniques can be used to essentially enlarge the stability region so that the resulting scheme behaves like an unconditionally stable scheme; while the diffusion subproblem is always self-adjoint and coercive so that they can be solved efficiently using many existing optimal preconditioned iterative solvers. The scheme can be extended for solving the Navier-Stokes equations, where the nonlinearity is resolved by a linear explicit multistep scheme at the convection step, while only a generalized Stokes problem is needed to solve at the diffusion step and the major stiffness matrix stays invariant in the time marching process. Numerical simulations are presented to demonstrate the stability, convergence and performance of the single-step and multistep variants of the new scheme.

Computation of Vortex Lock-In in the Laminar Wake of a Circular Cylinder Using Unsteady Monopole Sources

1995 ◽  
Vol 117 (2) ◽  
pp. 227-233 ◽  
Author(s):  
Dartzi Pan ◽  
Yu-Chi Chin ◽  
Chih-Hao Chang
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Laminar Wake ◽  
Lock In ◽  
Flux Difference

The vortex lock-in in the laminar wake behind a circular cylinder induced by the unsteady monopole source is numerically simulated in this paper. The artificial compressibility method is employed to solve the incompressible Navier-Stokes equations. A high-order accurate upwind flux-difference finite-volume scheme is used to discretize the flow field. The unsteady monopole source is simulated by a pulsating volume flux through the cylinder surface at a prescribed forcing frequency and amplitude. The forcing amplitude is set to a fixed value while the frequency is varied to search for the lock-in region. The flow field of the periodic lock-in state is examined in detail. Finally, the effects of a higher amplitude and a different source location are briefly investigated.

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