TIME-SPECTRAL EXTENSION TO AN IMPLICIT NAVIER–STOKES SOLVER: INTEGRATION AND EFFICIENCY ASPECTS

Abstract

The time-spectral method (TSM) promises a huge efficiency potential for engineering flows in which the solution can be expected to be predominantly periodic in time, such as flows through engines, wind turbines, helicopters or valves. For N harmonics in time, the TSM leads to a nonlinear equation system in the time domain governing a blocked state-vector composed of 2N + 1 steady-state like CFD solution vector blocks. The resulting large, sparse and blocked nonlinear equation systems require scalable and robust solution algorithms. We integrate the TSM in the CFD software CODA, a powerful and modular environment offering a wide range of models, discretization schemes and implicit solution algorithms. We discuss key aspects relevant for the integration of the TSM, focusing on the implicit solution strategy by means of nested algorithms of (non)linear solvers and linear preconditioners. The approach relies on a CFL-relaxed pseudo Newton-algorithm in combination with Krylov/GMRES schemes which, in turn, can be preconditioned by Block-Gauss–Seidel/Jacobi methods with a direct inversion of spatial/time-spectral element blocks. Moreover, a direct line-inversion approach based on the Thomas algorithm, which is provided by the base-line solver, is applied to the spatial/time-spectral line blocks of the TSM problem here. Different solver settings for the hierarchical solution method are investigated and discussed in terms of their efficiency for 2D and 3D aerodynamic TSM problems.