High-Performance C++ and Julia solvers in CADET for weakly and strongly coupled continuous chromatography problems

This study evaluates two numerical solvers for continuous chromatography: CADET-Core, implemented in C++, and CADET-Julia, implemented in Julia. Both codes can be used to model arbitrary networks of unit operations, including cyclic settings, and to solve the resulting strongly coupled systems accurately. Furthermore, the One-Column Analog (OCA) Fixed Point Iteration (FPI) method was implemented in CADET-Julia as a weak coupling alternative to the strongly coupled approach for Cyclic Steady State (CSS) simulations. We conducted extensive continuous chromatography benchmarks, comparing the C++ implementation of both a Discontinuous Galerkin Spectral Element Method (DGSEM) and a Finite Volume (FV) method with the Julia DGSEM implementation. The case studies encompass both full system dynamics from startup and CSS benchmarks. For the startup benchmarks, the Julia DGSEM implementation performed slightly better than the C++ implementation, and both performed significantly better than the C++ FV implementation. The C++ implementation scales better than the Julia implementation, resulting an computational advantage for large systems with many degrees of freedom. For the CSS benchmarks, the OCA-FPI approach performed best for spatial resolutions above a certain threshold, otherwise the strongly coupled approach using the Julia implementation was slightly faster.