Multi-domain DRM boundary element method for non-isothermal non-Newtonian Stokes flow with viscous dissipation

This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non-Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non-linear terms is converted into equivalent boundary integrals by the multi-domain dual reciprocity method (MD-DRM) in each subdomain. Augmented thin plate splines interpolation functions are used for the approximation of field variables. The iterative numerical formulation is achieved by viewing the material as divided into small elements and on each of them the integral representation formulae for the velocity and temperature are applied and discretised using linear boundary elements. The final system of non-linear algebraic equations is solved by a modified Newton's method The numerical examples include non-Newtonian problems with viscous dissipation, temperature-dependent viscosity and natural convection due to bouyancy forces.