Integral conditions on the vorticity  Numerical algorithms for the steady and unsteady NavierStokes equations
Abstract
A derivation of exact vorticity equations in the form of integrallike projection conditions as a counterpart to the stream function values assigned to the boundary for numerical solutions of the NavierStokes equation is presented. Basic equations are defined for the vorticity and stream function of the continuum equations as a set of two split equations. Discrete approximations and numerical algorithms are derived for the calculation of steady and unsteady flows using finite differences, with the assumption of a twolevel, timestepping scheme. The diffusion term is dealt with implicitly, while nonlinear advection is accounted for in increasing degrees of implicitness, depending on the linearization approximation used. One explicit and three implicit schemes are devised, together with one explicit and two implicit algorithms for producing spatial discretization. The algorithms are applied to the driven cavity flow problem in conditions of Re of 100 and 1000 and a time step of 0.5. Good agreement is found with experimentally determined data.
 Publication:

Numerical Methods in Laminar and Turbulent Flow
 Pub Date:
 1981
 Bibcode:
 1981nmlt.proc...79Q
 Keywords:

 Incompressible Flow;
 NavierStokes Equation;
 Steady Flow;
 Stream Functions (Fluids);
 Unsteady Flow;
 Vorticity Equations;
 Algorithms;
 Cavity Flow;
 Computational Fluid Dynamics;
 Discrete Functions;
 Ducted Flow;
 Flow Distribution;
 Flow Geometry;
 Time Dependence;
 Wall Flow;
 Fluid Mechanics and Heat Transfer