A Time Parallel Approach to Numerical Simulation of Asymptotically Stable Dynamical Systems with Application to CFD Models of Helicopter Rotors
A Time Parallel Approach to Numerical Simulation of Asymptotically Stable Dynamical Systems with Application to CFD Models of Helicopter Rotors
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Date
2023
Authors
Silbaugh, Benjamin Scott
Advisor
Baeder, James D
Citation
Abstract
Modern High Performance Computing (HPC) machines are distributed memoryclusters, consisting of multi-core compute nodes. Engineering simulation and
analysis tools must employ efficient parallel algorithms in order to fully
utilize the compute capability of modern HPC machines. The trend in
Computational Fluid Dynamcis (CFD) has been to construct parallel solution
algorithms based on some form of spatial domain decomposition. This approach has
been shown to be a success for many practical applications. However, as one
attempts to utlize more compute cores, limitations in strong scalability are
inevitably reached due to a diminishing compute workload per compute core and
either fixed or increasing communication cost. Furthermore, spatial domain
decomposition approaches cannot be easily applied to mid-fidelity structural
dynamics or rigid body dynamics models. A significant majority of industrial
fluid and structural dynamic models utilize some form of time marching. Thus, if
the domain decomposition strategy may be extended to include the temporal
dimension, additional opportunity for increased parallelism may be realized.
A new form of periodic multiple shooting is proposed that ismatrix-free and may be applied to high-fidelity multiphysics models or
other high dimensional systems. The proposed methodology is formulated entirely
in the time domain. Therefore, existing time-domain simulation tools may utilize
the proposed approach to achieve a high degree of distributed memory parallelism
without requiring any reformulation. Furthermore, the proposed methodology may be combined
with conventional space domain decomposition techniques and other forms of data
parallelism to achieve maximal performance on modern HPC architectures. The
proposed algorithm retains the iterative shoot-correct approach of conventational
periodic shooting methods. However, the correction stage is formulated using a
hierarchical evaluation strategy combined with an Arnoldi subspace approximation
to eliminate the need for explicit formulation of Jacobian matricies. The local
convergence of the proposed method is formally proven for the case of
an asyptotically stable dynamical system. The proposed method is numerically
tested for a 2D limit cycle problem, a rigid blade helicoper rotor model with
quasi-steady aerodynamics and autopilot trim, and an OVERSET CFD model of a
helicopter rotor with prescribed elastic blade motions. The method is observed
to be convergent in all test cases and found to exhibit good scalability.
The proposed periodic multiple shooting method is a practical means of reducingtime-to-solution for numerical simulations of asymptotically stable periodic
systems on distributed memory parallel computers. Furthermore, the proposed
method may be used to enhance the parallel scalability of OVERSET CFD models of
helicopter rotors in steady periodic flight.