A grid free method for approximating incompressible boundary layers is introduced. The computational elements are segments of vortex sheets. The method is related to the earlier vortex method; simplicity is achieved at the cost of replacing the Navier-Stokes equations by the Prandtl boundary layer equations. A new method for generating vorticity at boundaries is also presented; it can be used with the earlier vortex method. The applications presented include (i) flat plate problems, and (ii) a flow problem in a model cylinder-piston assembly, where the new method is used near walls and an improved version of the random choice method is used in the interior. One of the attractive features of the new method is the ease with which it can be incorporated into hybrid algorithms.
[1]
J. Marsden,et al.
A formula for the solution of the Navier-Stokes equations based on a method of Chorin
,
1974
.
[2]
Alexandre J. Chorin,et al.
Random choice methods with applications to reacting gas flow
,
1977
.
[3]
J. Marsden,et al.
Product formulas and numerical algorithms
,
1978
.
[4]
K. Stewartson.
ON GOLDSTEIN'S THEORY OF LAMINAR SEPARATION
,
1958
.
[5]
J. Glimm.
Solutions in the large for nonlinear hyperbolic systems of equations
,
1965
.
[6]
A. Chorin.
Numerical study of slightly viscous flow
,
1973,
Journal of Fluid Mechanics.
[7]
Alexandre J. Chorin,et al.
Random choice solution of hyperbolic systems
,
1976
.