Inside HEMSim algorithms: an interior-point-based method for non-linear constrained optimization applied to chemical equilibrium in highly energetic material simulations

In this paper, a new numerical algorithm for computing chemical equilibrium in highly energetic material simulations is presented. The method has been implemented in HEMSim (Highly Energetic Material Simulator), the thermochemical code developed at Politecnico di Torino for modeling detonation behavior. The proposed approach is based on an interior-point method applied to a computationally demanding nonlinear cost function defined through complex thermodynamic equations of state. A key feature of the method is the introduction of an enhanced stopping criterion that ensures convergence toward a true local minimum, eliminating the need for tentative phase addition or removal during or after the minimization process. This substantially improves robustness and computational efficiency, particularly for systems involving multiple condensed phases or incomplete reactions. Special attention is devoted to modeling the partial reaction of aluminum, a critical aspect in the analysis of modern aluminized explosives. The algorithm is validated through comparisons with MATLAB’s FMINCON interior-point routine, showing improved stability and accuracy while requiring fewer iterations. The resulting framework provides a reliable tool for chemical-equilibrium calculations.