Numerical solution of non-newtonian problems by the multi-domain dual reciprocity method

An efficient Boundary Element solution of the momentum equations for inelastic non-Newtonian fluids is presented in this paper. For the numerical solution all the domain integrals of the boundary element formulation have been transformed into equivalent boundary integrals by means of the Dual Reciprocity Method (DRM). Two major improvements have been made on the DEM, namely the use of augmented thin plate splines as interpolation functions, and the partition of the entire domain into smaller subrogions. In each sub-region or domain element the DRM was applied together with some additional equations that ensure continuity on the interfaces between adjacent sub-domains. This new method known as Multiple Domain Dual Reciprocity (MD-DRM) yields a sparse system of equations and a more localised approximation of the nonlinear terms than the traditional DRM. Several non-Newtonian problems were solved using the MD-DRM, including the pressure driven flow of a power law fluid, the Couette flow and two simulations of industrial polymer mixers.