ISSN:
0271-2091
Keywords:
incompressible flow
;
artificial compressibility
;
artificial bulk viscosity
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Peyret (J. Fluid Mech., 78, 49-63 (1976)) and others have described artificial compressibility iteration schemes for solving implicit time discretizations of the unsteady incompressible Navier-Stokes equations. Such schemes solve the implicit equations by introduing derivatives with respect to a pseudo-time variable τ and marching out to a steady state in τ. The pseudo-time evolution equation for the pressure p takes the form ∂p/∂ = -a2∂∇.u, where a is an artificial compressibility parameter and u is the fluid velocity vector. We present a new scheme of this type in which convergence is accelerated by a new procedure for setting a and by introducing an artificial bulk viscosity b into the momentum equation. This scheme is used to solve the non-linear equations resulting from a fully implicit time differencing scheme for unsteady incompressible flow. We find that the best values of a and b are generally quite different from those in the analogous scheme for steady flow (J. D. Ramshaw and V. A. Mousseau, Comput. Fluids, 18, 361-367 (1990)), owing to the previously unrecognized fact that the character of the system is profoundly altered by the pressence of the physical time derivative terms. In particular, a Fourier dispersion analysis shows that a no longer has the significance of a wave speed for finite values of the physical time step δt,. Inded, if on sets a ˜ |u| as usual, the artificial sound waves cease to exist when δt is small and this adversely affects the iteration convergence rate. Approximate analytical expressions for a and b are proposed and the benefits of their use relative to the conventional values a ∼ |u| and b = 0 are illustrated in simple test calculations.
Additional Material:
2 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650210205
