Boundary Integral Methods (BIM) have the advantage of greatly reducing the computational cost of numerical simulations by only discretizing the boundary of the problem thus reducing the problem dimensionality by one. However, BIM is often seen in disadvantage to domain methods when dealing with non linear problems as the non linear terms are usually treated as a domain integral of a pseudo body force that had to be solved by direct integration, making BIM based codes loose most of it advantages and increase computational cost even beyond Finite Element Methods (FEM).

Some alternatives such as the use of particular solutions and interpolation schemes such as the Dual Reciprocity Method (DRM) have been proposed to try and maintain the boundary only character of the method when dealing with non linear flow problems. These alternatives require the multiplication of fully populated matrices that require approximately 13*N³ operations where N is the total number of equations in the system thus greatly increasing computational cost without necessarily obtaining an accurate solution in strong non linear cases.

In this work, a novel Indirect Boundary Integral Formulation is presented for non linear flow problems, more specifically, the flow of a strongly shear thinning power law fluid inside a couette type mixer. By using an indirect approach the calculation of some of the integral matrices are not required, thus reducing computational cost even on the linear part of the problem. Later on, the non linear term is approximated by the use of particular solutions that modify the boundary conditions of the problem. In this way, the solution of the actual physical system is obtained by superimposing a homogeneous velocity field with a particular solution of the same field that accounts for the non linear terms in the original partial differential equation. Non linear terms are calculated implicitly using a Newton-Raphson based method for the non linear system of equations resulting after discretization of the resulting integral equation system. Using this method and standard Boundary Element Method meshes, accurate solutions for the coquette flow problem where obtained for values of the power law index as low as 0.6.