Additive–Multiplicative Regulators: Numerical Simulations from Laminar Flow to Cosmological Systems

In a preceding theoretical study, additive–multiplicative regulators (AM-regulators) were introduced as a structural framework governing how physical contributions accumulate across scale. That work demonstrated that classical mechanics, continuum fluid dynamics, and gravitational field equations can be embedded within a unified formulation in which additive source terms dominate locally, while multiplicative regulation emerges under large-scale accumulation—without altering the underlying laws of motion.

In this paper, we present a comprehensive numerical investigation of AM-regulated dynamics across representative physical regimes. The framework is implemented in simulations of laminar incompressible flow, strong-field gravitational configurations, and effective cosmological models relevant to dark matter and dark energy phenomenology. Numerical schemes are constructed to preserve conservation laws, dimensional consistency, and exact reduction to standard equations in the limit of vanishing regulation.

The simulations reveal a clear and robust separation of roles: additive regulators control local forcing and dissipation, while multiplicative regulators impose global, scale-sensitive modulation that constrains growth without inducing singular behavior. In fluid systems, this results in regulated stability and controlled transition behavior; in gravitational and cosmological settings, the same regulatory structure produces effective large-scale responses consistent with observed dark-sector phenomena, without the introduction of new fields or particles.

These results provide the first numerical validation of additive–multiplicative regulation as a viable cross-domain modeling framework, establishing it as a computationally stable and physically consistent extension of existing continuum and gravitational theories.