The Almansi Decomposition For Solving Direct
And Inverse Stokes Problems
Author(s)
A. E. Curteanu, L. Elliott, D. B. Ingham & D. Lesnic
Abstract
The solution of the equations governing the slow viscous fluid flow in two dimensions
is analysed using a novel technique based on a Laplacian decomposition.
This results in a set of three Laplace equations for pressure and two other auxiliary
harmonic functions which arise from the ideas of Almansi decomposition. These
equations, which become coupled through the boundary conditions, are numerically
solved using the Boundary Element Method (BEM). Numerical results for
both direct and inverse problem are presented and discussed considering a benchmark
test example in a circular domain.
1 Introduction
The Stokes equations describe fluid flows at low Reynolds number when the viscous
forces dominate over the inertial forces. These laminar flows are important in
flows in pipes and open channels, seepage of water and oil underground, for very
small bodies, such as small spheres, in a highly viscous fluid, in the theory of lubrication,
etc. During the last few decades there has been some interest in applying
the BEM for the solution of Stokes flow problems, e.g. see Higdon [3], Zeb et al.
[7], Lesnic et al. [8].
2 Mathematical formulation
The Navier-Stokes equations of motion are mathematical statements of the dynamical
conditions within a viscous fluid flow, and as such are expected to accurately
apply to each and every problem involving a laminar viscous fluid flow. However,
due to the mathematical complexity of the equations, it is well known that the
general solution of these equations is not possible. Therefore in order to construct
Keywords
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