# On the use of Green’s formula for the solution of the Navier-Stokes equations

## Abstract

A general iterative procedure for solving Navier-Stokes system in stream function-vorticity variables  is considered. Using the fundamental solution for Laplace operator we find a boundary condition for vorticity. We define an application such that the vorticity is its fixed point. In order to construct this application we solve a Dirichlet problem for Laplace equation and a boundary value problem for vorticity equation in divergence form. A FEM and a classical BEM are used to accomplish this task. Some numerical experiments are carried out.

## Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

## Keywords

Navier-Stokes system; stream function; vorticity; Laplace operator; fundamental solution; iterative solver; FEM; BEM;

### References

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## Cite this paper as

C.I. Gheorghiu, On the use of Green’s formula for the solution of the Navier-Stokes equations, Adv. Water Resources, 14 (1991) 113-117
doi: 10.1016/0309-1708(91)90002-6

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Elsevier

0309-1708

1573-1634

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