The convergence of explicit schemes in NavierStokes equations
Abstract
An analysis is made of a class of explicit difference schemes for solving NavierStokes equations in stream functionvortex variables with parametric approximations of nonlinear terms and vortex values at the boundaries. A priori estimates of grid solutions are obtained, and their convergence to a generalized solution is proved. Formulas are presented for calculating the interval of a nonuniform temporal grid as a function of the instantaneous values of the grid Reynolds number and of the type of boundary conditions for the vortex. The convergence rate of the schemes in the presence of sufficiently smooth solutions is investigated.
 Publication:

Zhurnal Vychislitelnoi Matematiki i Matematicheskoi Fiziki
 Pub Date:
 June 1984
 Bibcode:
 1984ZVMMF..24..876K
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 NavierStokes Equation;
 Stokes Flow;
 Stream Functions (Fluids);
 Vorticity Equations;
 Boundary Conditions;
 Boundary Value Problems;
 Computational Grids;
 Convergence;
 Parameter Identification;
 Reynolds Number;
 Two Dimensional Flow;
 Fluid Mechanics and Heat Transfer