ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Method of linearizing computational fluid dynamics model and its applications
Received date: 2014-11-17
Revised date: 2015-01-30
Online published: 2015-03-20
Supported by
National Basic Research Program of China (6132400101)
Computational fluid dynamics (CFD) is not just a simulation method, but a kind of complicated mathematical model for fluid flows. In the fields like flow stability analysis, aeroelastic analysis, aerodynamic optimization and flow control, from the viewpoint of dynamics system, the system matrix of a CFD model can be constructed for quantitative analysis, obtaining more systematic information about the CFD model. However, CFD model is a complicated high order nonlinear system. It is difficult to construct the system matrix directly. In this paper, automatic differential method is cooperated with manual coding to construct the Jacobian of a parallel finite volume CFD solver based on multiblock structured grid. Automatic differential is applied to obtaining the local Jacobian of the flux across each interface. And by means of manual coding, each local Jacobian is assembled into the global distributed sparse Jacobian. In order to solve the linearized system, preconditioned GMRES method is adopted. In the parallel environment, the block Jacobi preconditioner is used while ILU(0) preconditioner is applied to each parallel thread. In the numerical tests, this procedure is applied to ① constructing and solving the linear system of an unsteady flow around NACA0012 airfoil; ② sensitivity analysis based on the adjoint equation for a steady flow of NACA0012 airfoil; ③ reduced order modeling for the aeroelastic problem of AGARD wing 445.6. The results agree excellently with the data of CFD simulations.
QU Kun , LI Jichao , CAI Jinsheng . Method of linearizing computational fluid dynamics model and its applications[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015 , 36(10) : 3218 -3227 . DOI: 10.7527/S1000-6893.2015.0035
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