A non-conforming computational methodology for modeling coupled problems

A variety of engineering applications that involve coupling different physical phenomena, often require detailed finite element analysis to be carried out over complex domains. Often such analysis, may be accomplished by dividing the global domain into several local sub-domains over each of which, a local model can be analyzed independently. The global solution can then be constructed by suitably piecing together local solutions from these individually modeled sub-domains. However, during the assembly, it is often too cumbersome, or even infeasible, to coordinate the meshes over separate sub-domains. One must therefore, employ non-conforming techniques to accomplish such modeling. In this paper, we develop a non-conforming computational methodology via the mortar finite element method to solve a coupled problem where we are interested in determining the effects of temperature variations on a given flow or the transfer of heat within the flow. Using this method the solution over different sub-domains with different multigrid levels is efficiently computed. Our numerical results clearly suggest that the proposed methodology is robust and stable.