Nonlinear acceleration of coupled fluid–structure transient thermal problems by Anderson mixing

Abstract

SUMMARY Conjugate heat‐transfer problems are typically solved using partitioned methods where fluid and solid subdomains are evaluated separately by dedicated solvers coupled through a common boundary. Strongly coupled schemes for transient analysis require fluid and solid problems to be solved many times each time step until convergence to a steady state. In many practical situations, a fairly simple and frequently employed fixed‐point iteration process is rather ineffective; it leads to a large number of iterations per time step and consequently to long simulation times. In this article, Anderson mixing is proposed as a fixed‐point convergence acceleration technique to reduce computational cost of thermal coupled fluid–solid problems. A number of other recently published methods with applications to similar fluid–structure interaction problems are also reviewed and analyzed. Numerical experiments are presented to illustrate relative performance of these methods on a test problem of rotating pre‐swirl cavity air flow interacting with a turbine disk. It is observed that performance of Anderson mixing method is superior to that of other algorithms in terms of total iteration counts. Additional computational savings are demonstrated by reusing information from previously solved time steps. Copyright © All rights reserved 2012 Rolls‐Royce plc.

Coupled Fluid-Structure Transient Thermal Analysis of a Gas Turbine Internal Air System With Multiple Cavities

“…12 and 13. The results illustrate a clear algorithmic advantage 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 0 Our current FORTRAN implementation of the method written as an interface solver between SC03 and HYDRA codes is able to reproduce the performance benefits observed in [17] on a large industrial scale model coupled to five cavities.…”

“…Detailed performance analysis of the method with application to the conjugate heat transfer problems is given in [17]. The procedure starts with an initial guess of the interface temperature field T n+1 Σ,0 applied as a boundary condition to the fluid solver.…”

Multi-level acceleration with manifold mapping of strongly coupled partitioned fluid–structure interaction

“…The IQN-ILS technique [16] is an efficient [17,3] and robust black-box coupling algorithm for which convergence theorems are available in [18]. The IQN-ILS algorithm is mathematically equivalent to Anderson acceleration [19,20,21] which can be categorized as a multisecant method as discussed by Fang and Saad [22]. When applied to linear problems, it can be shown that Anderson acceleration is essentially equivalent to the GMRES method [20], which has also been shown for the IQN-ILS method [23].…”

“…if converged then mapping matrix T k does not need to be initialized with the identity matrix at line 2, but can be determined with (21). The mapping matrix T k is of size n × n which can be prohibitively large for large scale applications.…”

“…Anderson acceleration [19,20,21] is used to solve the optimization problem of the coarse model (16). Anderson acceleration is mathematically equivalent to the IQN-ILS technique [16].…”