Cross-compatibility of First-order Numerical Integrations in Jacobi Method Co-simulation Systems

Non-iterative co-simulation is an essential method for complex multi-physics systems. Adopting this technique enables the ability to use computational resources. As the physics of systems differ, the numerical solution of their governing equations may differ. As the numerical integration for each subsystem changes, the information between subsystems will change, making the error after each interaction step between subsystems. This paper examines the compatibility of numerical approximations by error examination of the solution compared with the exact solution. A mass-spring-damper system as benchmark problem considered, and two scenarios of system properties are made. The governing equations of each subsystem in the problem are separated, and the Jacobi orchestration of co-simulation is configured. The error results show that the best compatibility between first-order numerical integrations happens when the slow subsystem integration is backward Euler, and the fast subsystem uses semi-implicit Euler. Results also show that the energy loss terms in the systems equations make no changes in the main result. On the other hand, the energy loss terms change the average simulation duration.