Accuracy and stability analysis of a second‐order time‐accurate loosely coupled partitioned algorithm for transient conjugate heat transfer problems

Abstract

SUMMARYIn this paper, a second‐order time‐accurate loosely coupled partitioned algorithm is presented for solving transient thermal coupling of solids and fluids, also referred to by conjugate heat transfer. The Crank–Nicolson scheme is used for time integration. The accuracy and stability of the loosely coupled solution algorithm are analyzed analytically. Based on the accuracy analysis, the design order of the time integration scheme is preserved by following a predictor (implicit)–corrector (explicit) approach. Hence, the need to perform an additional implicit solve (a subiteration) at each time step is avoided. The analytical stability analysis shows that by using the Crank–Nicolson scheme for time integration, the partitioned algorithm is unstable for large Fourier numbers, unlike the monolithic approach. Accordingly, using the stability analysis, a stability criterion is obtained for the Crank–Nicolson scheme that imposes restriction on Δt given the material properties and mesh spacings of the coupled domains. As the ratio of the thermal effusivities of the coupled domains reaches unity, the stability of the algorithm reduces. To demonstrate the applicability of the algorithm, a numerical example is considered (an unsteady conjugate natural convection in an enclosure). Copyright © 2013 John Wiley & Sons, Ltd.

A numerical method for multiphysics simulations based on hierarchical Cartesian grids

“…Examples thereof include a LES of an aeronautical combustor (Jaure et al, 2013), unsteady conjugate natural convection in an enclosure (Kazemi-Kamyab et al, 2014), and the modeling of an inertial-confinement-fusion hohlraum target as well as the flow of coolant past an hexagonal array of heated fuel rods (Henshaw and Chand, 2009).…”

On the Stability of Loose and Strong Partitioned Algorithms for Thermal Coupling of Domains Using Higher Order Implicit Time Integration Schemes

“…By expressing the predictor-corrector θ scheme, used in [5] for solving unsteady CHT problems, in terms of a two-stage IMEX scheme (its butcher tableau is given in Table 2), …”

“…In the results section, the stability of the algorithm, with the explicit corrector step included, is investigated numerically. The full details of the stability analysis is presented in [5].…”

“…By considering the asymptotic solution to z under this assumptions, it is noted that for θ = 0.5, the algorithm is unstable (see [5]). On the other hand, for Backward Euler (θ = 1), the algorithm is unconditionally stable.…”

“…In [5], it is reasoned that σ est defined in (7) (the ratio between thermal effusivities of the domains) can be used as a measure of the physical strength of the coupling. Therefore, when σ est ≪ 1, the coupling is referred to as physically weak and as σ est → 1 the strength of the coupling increases.…”