Optimization of the Deflated Conjugate Gradients algorithm applied to the massively parallel LES of heat transfer in gas turbines

摘要

The study of heat transfers requires computations on very fine meshes, and the discretization of the Navier-Stokes equations at low-Mach number on such meshes induces the solving of symmetric linear systems with up to billions of unknowns. Here, a two-level method is first presented, that uses an arbitrary coarse grid to reduce computational costs for this solving. However, the coarse grid generated can count up to millions of cells: direct solvings on this level are thus out of reach, but iterative solvings involve a large number of communications, dramatically impairing parallel performances. To this effect, two methods are developed in order to reduce the number of iterations on the coarse level, that are easy to implement in any adequately designed Deflated Conjugate Gradients solver. Using this novel method, computational times for massively parallel simulations of a turbulent flow around a turbine blade are decreased by up to 49%.