An optimization task with nonlinear differential-algebraic equations (DAEs) was approached. In special cases in heat and mass transfer engineering, a classical direct shooting approach cannot provide a solution of the DAE system, even in a relatively small range. Moreover, available computational procedures for numerical optimization, as well as differential- algebraic systems solvers are characterized by their limitations, such as the problem scale, for which the algorithms can work efficiently, and requirements for appropriate initial conditions. Therefore, an αDAE model optimization algorithm based on an α-model parametrization approach was designed and implemented. The main steps of the proposed methodology are: (1) task discretization by a multiple-shooting approach, (2) the design of an α-parametrized system of the differential-algebraic model, and (3) the numerical optimization of the α-parametrized system. The computations can be performed by a chosen iterative optimization algorithm, which can cooperate with an outer numerical procedure for solving DAE systems. The implemented algorithm was applied to solve a counter-flow exchanger design task, which was modeled by the highly nonlinear differential-algebraic equations. Finally, the new approach enabled the numerical simulations for the higher values of parameters denoting the rate of changes in the state variables of the system. The new approach can carry out accurate simulation tests for systems operating in a wide range of configurations and created from new materials.
Multiple Shooting for Unstructured Nonlinear Differential-Algebraic Equations of Arbitrary Index
