Damped artificial compressibility iteration scheme for implicit calculations of unsteady incompressible flow

Peyret 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 introducing 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/∂τ = -a 2 ⊇.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.

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