A high order time-accurate loosely-coupled solution algorithm for unsteady conjugate heat transfer problems

•For conjugate heat transfer, a high order loosely-coupled solution algorithm is presented.•High order IMEX Runge–Kutta schemes are used for time integration.•Temporal design order is preserved without the need for subiterating.•For thermally weak couplings, time step-size is restricted by accuracy, not stability.•Computational efficiency relative to Crank–Nicolson and BDF2 schemes is observed. Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Noting that time-accurate computations of transient CHT problems can be computationally expensive, we consider the use of high order implicit time integration schemes which have the potential to be computationally more efficient relative to the commonly used second order implicit schemes. For thermally weak couplings, we present a loosely-coupled solution algorithm where high order implicit–explicit (IMEX) Runge–Kutta schemes are employed for time integration. The IMEX schemes consist of the explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) schemes, for advancing the solution in time within each separate fluid and solid subdomain, and the explicit Runge–Kutta (ERK) schemes, for explicit integration of part of the coupling terms. By considering a numerical example (an unsteady conjugate natural convection in an enclosure), temporal order preservation of the coupling algorithm (without subiterating) is demonstrated. In addition, the stability of the loosely-coupled algorithm is investigated numerically for the CHT test-case; when the ratio of the thermal effusivities of the fluid and solid subdomains is much smaller than unity, using large Fourier numbers of the subdomains is possible, indicating that time-step size is restricted by accuracy rather than stability. Furthermore, the (computational) work-(temporal) precision character of several time integration schemes in solving the CHT test-case is compared over a range of accuracy requirements; for time-accurate solutions, the fourth and fifth order IMEX schemes are 1.5 times more efficient than Crank–Nicolson and 2.7 times more efficient than BDF2. The computational gain is higher for smaller tolerances.