J. Comp. Math., 8 (1990), pp. 276-288.


On An Unconditionally Stable Scheme For The Unsteady Navier-Stokes Equations

Jie Shen 1

1 Department of Mathematics, Indiana University, USA

Received 1988-1-11 Revised Online 2006-12-10

Abstract

Theoretical time step constraints of semi-implicit schemes are known to be more restrictive than should be in pratice. We intend to alleviate the constraints with more smoothmess assumptions on the solutions. Bt introducing a new scheme with modification on the treatment of the nonlinear term, we are able to prove that the scheme is unconditionally stable and convergent. Further more, we show that the modified scheme and the original semi-implicit one are equivalent under a weak condition on the time step and the number of space discretization points.

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