Numerical solution of the incompressible NavierStokes equations about arbitrary twodimensional bodies
Abstract
A method of automatic numerical generation of general curvilinear coordinate system having a constant coordinate line coincident with each boundary of a general multiconnected physical flow region was developed. These curvilinear coordinates are generated as the solution of two elliptic partial differential equations with Dirichlet boundary conditions. Once the natural coordinates are generated for a given physical domain, the vorticitystream function formulation of the NavierStokes equations are transformed to the rectangular transformed plane. The equations were approximated using central differences for the space derivatives and a backward firstorder time difference for the vorticity time derivative. The flow solution is carried out by an implicit method with SOR iteration being used to converge the elliptic space variation at each time step. The vorticity distribution on the body surface is calculated at each time step utilizing a modified multidimensional false position iteration designed to force the tangential velocity component on the body surface to zero. Dirichlet conditions corresponding to irrotational flow were used at the remote boundary.
 Publication:

Ph.D. Thesis
 Pub Date:
 1975
 Bibcode:
 1975PhDT........33T
 Keywords:

 Incompressibility;
 NavierStokes Equation;
 Numerical Analysis;
 Two Dimensional Bodies;
 Cartesian Coordinates;
 Dirichlet Problem;
 Vorticity Equations;
 Fluid Mechanics and Heat Transfer