This work introduces the hydrodynamic approximation and the continuum limit of the triadic network within the framework of Triadic Mesh Dynamics (TMD). It demonstrates that the discrete orientational interactions of triads converge, under the assumption of a sufficiently fine and statistically isotropic network, to the Laplace operator. The resulting effective wave equation provides a macroscopic description of triadic dynamics, including an emergent propagation speed and a dissipative term corresponding to the microscopic forgetting mechanism. The paper further presents a practical implementation of this continuum approximation in standard PDE‑based simulation tools such as COMSOL Multiphysics and FEniCS. This creates a functional bridge between the discrete microscopic model of TMD and the continuous numerical methods used in experimental physics. The work thus provides a foundation for realistic simulations of experiments such as the orientational shadow method for probing the internal structure of baryons.
Aleš Kováč (Tue,) studied this question.