The paper is organized as follows. In Section 2 we introduce the model describing a mDWC in Detail. We describe the used MESH equations and introduce an thermodynamically equivalent Petlyuk sequence. In the next section we describe the new solution approach. We first describe the general procedure and show how all process variables can be calculated from the chosen optimization variables. At the end of this section we introduce conditions which ensure that all values for the calculated concentrations remain positive. After a short description of the implementation details we present numerical results for different use cases in Section 5. First considering simple dividing wall columns, then for multiple dividing wall columns.