WIT Press

The Almansi Decomposition For Solving Direct And Inverse Stokes Problems


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WIT Press


A. E. Curteanu, L. Elliott, D. B. Ingham & D. Lesnic


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