Iterated linear programming strategies for nonsmooth simulation: Continuous and mixed-integer approaches

Abstract

With recent advances in computer hardware and software, more process simulation strategies are now being considered in an equation-oriented mode. This simulation mode relies on an equation solving engine which must deal effectively with nonsmooth and constrained relations which are often enforced as procedures in the sequential modular mode. Also, with complex flowsheet topologies and output specifications due to design or optimization calculations conditional and nonsmooth relations introduce derivative discontinuities into the problem which frequently cause these solvers to fail. In an earlier paper (Bullard and Biegler, Computers chem Engng 15, 4, 1991) we introduced an iterated linear programming (LP) based approach for solving the constrained simulation problem. The present article proposes two related approaches to handle a general class of nonsmooth problems. The first uses continuous variables while the second also includes binary variables. These approaches are demonstrated on a number of examples, includi pipeline network flow problems containing check valves which may either be on or off, flow transitions from laminar to turbulent and equidistribution problems which minimize the absolute value of the approximation error.