Regularization of the Logarithmic Mean for Robust Numerical Simulation

To calculate the driving temperature difference between hot and cold side of a heat exchanger, use logarithmic mean is common practice. provide high robustness in complex dynamic system models, robust formulation (logmean) function becomes vital. As analytic definition logmean naturally comes along with singularities limitations for specific input conditions, it essential to extend modify exchanger modeling. This paper proposes how can be extended valid all four quadrants Cartesian coordinate bridge resulting gaps. Special focus lies on such way that easily handled by numerical solvers. includes approximation its integral form implicit ODE solvers variable step width. Furthermore presented flatten steep gradients vicinity x- y-axes without manipulating uncritical regions. All modifications are finally applied simple simulation model written object-oriented programming language Modelica examine approach.