A Rewriting-Logic-Based Technique for Modeling Thermal Systems

Abstract

This paper presents a rewriting-logic-based modeling and analysis technique for physical systems, with focus on thermal systems. The contributions of this paper can be summarized as follows: (i) providing a framework for modeling and executing physical systems, where both the physical components and their physical interactions are treated as first-class citizens; (ii) showing how heat transfer problems in thermal systems can be modeled in Real-Time Maude; (iii) giving the implementation in Real-Time Maude of a basic numerical technique for executing continuous behaviors in object-oriented hybrid systems; and (iv) illustrating these techniques with a set of incremental case studies using realistic physical parameters, with examples of simulation and model checking analyses

Formal modeling and analysis of interacting hybrid systems in HI-Maude: What happened at the 2010 Sauna World Championships?

“…On the other hand, Euler is the computationally fastest, whereas RK4 is the slowest. The experiments in [7,22] indicate, for the one example, that RK2 is a good compromise between precision and efficiency. The "step size" (or "time increment") between each visited point in time is the parameter of these approximation methods; the smaller the step size, the more accurate the numerical approximation, and the longer the computation time.…”

“…The papers [7,22] show the execution times and the relative errors for the different numerical methods on an example that does have an analytical solution, i.e., when we can compute the solved form of the differential equations. RK4 is the most sophisticated approximation algorithm of these, and Euler is the least sophisticated one.…”

“…This execution is based on adaptations of the Euler [7], the Runge-Kutta 2nd order (RK2), and the Runge-Kutta 4th order (RK4) numerical approximation methods [22] to the effort/flow framework. The papers [7,22] show the execution times and the relative errors for the different numerical methods on an example that does have an analytical solution, i.e., when we can compute the solved form of the differential equations.…”

“…HI-Maude is based on the modeling methodology introduced in [7], which adapts the effort/flow method [19] to model a physical system as a network of physical entities and physical interactions between the entities. This approach is applicable to different areas of physical systems.…”

“…Non-compositional specification of the whole system is very hard, as it involves combining the ordinary differential equations (ODEs) that specify the dynamics of its components; it also requires redefining the system's continuous dynamics for each new configuration of interacting physical components. To achieve the desired modularity and compositionality, HI-Maude offers an object-oriented modeling methodology [7] that allows us to specify the continuous dynamics of single physical entities (such as the cup of coffee and the room) and of single physical interactions (such as thermal conduction and convection). Not only does this decomposition make it easier to specify the continuous dynamics of a system of interacting physical components, but it also means that the specification does not need to be redefined for each new configuration of physical entities.…”