Is the steady viscous incompressible two‐dimensional flow over a backward‐facing step at Re = 800 stable?

Abstract

SUMMARYA detailed case study is made of one particular solution of the 2D incompressible Navier-Stokes equations. Careful mesh refinement studies were made using four different methods (and computer codes): (1) a high-order finite-element method solving the unsteady equations by time-marching; (2) a high-order finite-element method solving both the steady equations and the associated linear-stability problem; (3) a second-order finite difference method solving the unsteady equations in streamfunction form by time-marching; and (4) a spectral-element method solving the unsteady equations by time-marching. The unanimous conclusion is that the correct solution for flow over the backward-facing step at Re=800 is steady-and it is stable, to both small and large perturbations.

Numerical Simulation of Pulse-Tube Refrigerators

“…We are interested in the time-dependent simulation of a flow that starts instantaneously. The problem is described by the Navier-Stokes equations for unsteady incompressible viscous flow At the inlet, the velocity has a parabolic profile: Figure 4.10, is qualitatively in good agreement with the time history plots of the streamwise velocity component given by Gresho et al [22].…”

“…There have been many numerical and experimental studies investigating this type of flow, see [1], [5], [19], [22]. This is one of the simplest geometrical cases that provides an interesting, non-trivial flow.…”

Fast solvers for discretized Navier-Stokes problems using vector extrapolation

“…Note that for this specific value of ν the flow is close to the stability limit which marks the transition from steady to unsteady flow. 1 A full discussion of this flow problem can be found in Gresho et al [8]. The spatial resolution is such that the solution does not change in the "eyeball" norm when using a finer grid.…”

Resolution of Unsteady Navier-stokes Equations with the C a,b Boundary condition

“…Using our solver, we run two traditional test problems (driven cavity flow [9,14,15,16,17], Backwardfacing step problem [10,13]) and the flow over an obstacle [9] with a number of different model parameters. 48 | P a g e www.ijacsa.thesai.org The Neumann condition is applied at the outflow boundary (x=5; −1 < y < 1) and automatically sets the mean outflow pressure to zero.…”