We present an approximation method for the non-stationary nonlinear in- compressible Navier-Stokes equations in a cylindrical domain （0, T） x G, where G C ]R3 is a smoothly bounded domain. Our method is applicable t...We present an approximation method for the non-stationary nonlinear in- compressible Navier-Stokes equations in a cylindrical domain （0, T） x G, where G C ]R3 is a smoothly bounded domain. Our method is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence, uniqueness and rep- resentation results from mathematical fluid dynamics. After a suitable time delay in the nonlinear convective term v. ~7v we obtain globally （in time） uniquely solvable equations, which - by using semi-implicit time differences - can be transformed into a finite number of Stokes-type boundary value problems. For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out. The method is reported in short outlines ranging from approximation theory up to numerical test calculations.展开更多
文摘We present an approximation method for the non-stationary nonlinear in- compressible Navier-Stokes equations in a cylindrical domain （0, T） x G, where G C ]R3 is a smoothly bounded domain. Our method is applicable to general three-dimensional flow without any symmetry restrictions and relies on existence, uniqueness and rep- resentation results from mathematical fluid dynamics. After a suitable time delay in the nonlinear convective term v. ~7v we obtain globally （in time） uniquely solvable equations, which - by using semi-implicit time differences - can be transformed into a finite number of Stokes-type boundary value problems. For the latter a boundary element method based on a corresponding hydrodynamical potential theory is carried out. The method is reported in short outlines ranging from approximation theory up to numerical test calculations.
