The numerical solution of incompressible NavierStokes equations
Abstract
During this period, research continued in the area of numerical solution of the incompressible NavierStokes equations. In particular, the following topics have been addressed: (1) The question of achieving stable discretizations of the imcompressibility constraint; (2) The problem of obtaining accurate solutions in the limit of large Reynolds numbers; and (3) Devising efficient numerical solution algorithms for solving the nonlinear algebraic systems of equations arisings from the discretization step. A necessary condition for convergence of the discrete approximation was obtained. A major result achieved has been to show that many often used low order element pairs are, in fact, unstable in the sense of this criterion. In addition, new simple low order element pairs were introduced and proved to be stable. Concerning the second topic noted above, the investigator has taken an approach based on the idea that h (the discretization parameter) needs to be small only in certain locations, namely in boundary layers. Finally, solving the algebraic systems which arise from the discretization remains a major difficulty. Two new approaches have been developed, one dependent on time marching to the steady state limit, and the other based on an adaptation of a method used in structural mechanics to the fluids case. Four new scientific papers have been generated in the report period, to be published in the referred literature.
 Publication:

Interim Technical Report
 Pub Date:
 May 1983
 Bibcode:
 1983cmu..rept.....N
 Keywords:

 Algebra;
 Incompressible Boundary Layer;
 NavierStokes Equation;
 Problem Solving;
 Algorithms;
 Nonlinear Systems;
 Research Management;
 Reynolds Number;
 Fluid Mechanics and Heat Transfer