The structured modeling framework of anaerobic digestion in Modelica: development of ADMLib package

This paper presents the development of ADMLib, a new high-productivity and efficient Modelica package to model and simulate anaerobic digestion systems inside the structured modeling framework. Library components were organized into subpackages to encompass growth kinetics, non-biochemical reaction kinetics, acid-base, heat transfer, and inhibition processes, as well as the characteristics of substances and gas phase. A validation of the dynamic behavior response was performed where the implemented functions were used to simulate different bibliographic models. A brief performance analysis was carried out, in order to evaluate the component-based approach of ADMLib against the traditional differential algebraic equation (DAE) systems. The implementation testing demonstrated that the developed package was reliable, usable, and performant.

A New Block Structural Index Reduction Approach for Large-Scale Differential Algebraic Equations

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications has emerged and became widely accepted; they generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAE systems with large dimensions, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on the Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameters has been presented. It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples, and preliminary numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.