  This work introduces a general framework for constructing high-order,
linearly stable, partitioned solvers for multiphysics problems from a
monolithic implicit-explicit Runge-Kutta (IMEX-RK) discretization of the
semi-discrete equations. The generic multiphysics problem is modeled as a
system of n systems of partial differential equations where the ith subsystem
is coupled to the other subsystems through a coupling term that can depend on
the state of all the other subsystems. This coupled system of partial
differential equations reduces to a coupled system of ordinary differential
equations via the method of lines where an appropriate spatial discretization
is applied to each subsystem. The coupled system of ordinary differential
equations is taken as a monolithic system and discretized using an IMEX-RK
discretization with a specific implicit-explicit decomposition that introduces
the concept of a predictor for the coupling term. We propose four coupling
predictors that enable the monolithic system to be solved in a partitioned
manner and preserve the IMEX-RK structure and therefore the design order of
accuracy of the monolithic scheme. The four partitioned solvers that result
from these predictors are high-order accurate, allow for maximum re-use of
existing single-physics software, and two of the four solvers allow the
subsystems to be solved in parallel at a given stage and time step. We also
analyze the stability of a coupled, linear model problem and show that one of
the partitioned solvers achieves unconditional linear stability, while the
others are unconditionally stable only for certain values of the coupling
strength. We demonstrate the performance of the proposed partitioned solvers on
several classes of multiphysics problems including a simple linear system of
ODEs, advection-diffusion-reaction systems, FSI problems, and particle-laden
flows.
