ACTA AERONAUTICAET ASTRONAUTICA SINICA >
Accelerated convergence method for fluid dynamics solvers based on reduced⁃order model and gradient optimization
Received date: 2022-03-01
Revised date: 2022-04-24
Accepted date: 2022-07-14
Online published: 2022-07-21
Supported by
National Natural Science Foundation of China(92152301)
Computational Fluid Dynamics（CFD）is an important method to solve fluid-related complex engineering problems. The increasing complexity of fluid mechanics research and engineering applications makes it imperative to explore a more efficient and accurate CFD algorithm. A method based on reduced-order model and gradient optimization is proposed to accelerate the convergence process of fluid dynamics solvers. In this method，the reduced-order model is constructed by the snapshots collected from the iterative process of CFD solvers，and the gradient optimization method is then used to minimize the residual of the reduced-order model. Finally，the flow field with lower residual is selected as the initial condition of the CFD solver to accelerate the convergence process of CFD. The method is applied to the CFD solver based on the finite volume method，and the effectiveness of the proposed method is studied for inviscid and turbulence fluids. The results show that the accelerated convergence method can significantly reduce the number of iterative steps by 2⁃3 times compared with the initial CFD method，exhibiting efficiency，robustness，and a wide application prospect in complex engineering problems.
Wenbo CAO , Yilang LIU , Weiwei ZHANG . Accelerated convergence method for fluid dynamics solvers based on reduced⁃order model and gradient optimization[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023 , 44(6) : 127090 -127090 . DOI: 10.7527/S1000-6893.2022.27090
| 1 | JAMESON A， BAKER T J. Solution of the Euler equations for complex configurations［C］∥ 6th Computational Fluid Dynamics Conference Danvers. Reston： AIAA， 1983. |
| 2 | GHIA U， GHIA N K， SHIN T C， et al. High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method［J］. Journal of Computational Physics， 1982， 48（3）： 387-411. |
| 3 | JAMESON A， SCHMIDT W， TURKEL E. Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes［C］∥ 14th Fluid and Plasma Dynamics Conference. Reston： AIAA， 1981. |
| 4 | TURKEL E. Preconditioned methods for solving the incompressible and low speed compressible equations［J］. Journal of Computational Physics， 1987， 72（2）： 277-298. |
| 5 | WYNN P. Acceleration techniques for iterated vector and matrix problems［J］. Mathematics of Computation，1962， 16（79）： 301-322. |
| 6 | BREZINSKI C. Generalisations de la transformation de shanks，de la table de Pade et de l'ε-algorithme［J］. Calcolo， 1975， 12（4）： 317-360. |
| 7 | CABAY S， JACKSON L W. A polynomial extrapolation method for finding limits and antilimits of vector sequences［J］. SIAM Journal on Numerical Analysis， 1976，13（5）： 734-752. |
| 8 | EDDY R P. Extrapolating to the limit of a vector sequence［J］. Information Linkage Between Applied Mathematics and Industry， 1979： 387-396. |
| 9 | MESINA M. Convergence acceleration for the iterative solution of the equations X=AX+f［J］. Computer Methods in Applied Mechanics and Engineering， 1977， 10（2）： 165-173. |
| 10 | SMITH D A， FORD W F， SIDI A. Extrapolation methods for vector sequences［J］. SIAM Review， 1987， 29（2）： 199-233. |
| 11 | SIDI A. Review of two vector extrapolation methods of polynomial type with applications to large-scale problems［J］. Journal of Computational Science， 2012， 3（3）： 92-101. |
| 12 | ARNOLDI W E. The principle of minimized iterations in the solution of the matrix eigenvalue problem［J］. Quarterly of Applied Mathematics， 1951， 9（1）： 17-19. |
| 13 | SAAD Y， SCHULTZ M H. GMRES：A generalized minimal residual algorithm for solving nonsymmetric linear systems［J］. SIAM Journal on Scientific and Statistical Computing， 1986， 7（3）： 856-869. |
| 14 | HAFEZ M， PARLETTE E， SALAS M. Convergence acceleration of iterative solutions of Euler equations for transonic flow computations［J］. Computational Mechanics， 1986， 1（3）： 165-176. |
| 15 | DJEDDI R， KAMINSKY A， EKICI K. Convergence acceleration of fluid dynamics solvers using a reduced-order model［J］. AIAA Journal， 2017，55（9）： 3059-3071. |
| 16 | SCHMID P J. Dynamic mode decomposition of numerical and experimental data［J］. Journal of Fluid Mechanics，2010， 656： 5-28. |
| 17 | SCHMID P J， LI L， JUNIPER M P，et al. Applications of the dynamic mode decomposition［J］. Theoretical and Computational Fluid Dynamics， 2011，25（1）： 249-259. |
| 18 | LIU Y， WANG G， YE Z Y. Dynamic mode extrapolation to improve the efficiency of dual time stepping method［J］. Journal of Computational Physics， 2018， 352：190-212. |
| 19 | ANDERSSON N. A non-intrusive acceleration technique for compressible flow solvers based on dynamic mode decomposition［J］. Computers & Fluids， 2016， 133： 32-42. |
| 20 | LIU Y， ZHANG W， KOU J. Mode multigrid-a novel convergence acceleration method［J］. Aerospace Science and Technology， 2019， 92： 605-619. |
| 21 | TAN S L， LIU Y L， KOU J Q， et al. Improved mode multigrid method for accelerating turbulence flows［J］. AIAA Journal， 2021， 59（8）： 3012-3024. |
| 22 | LUCIA D J， BERAN P S， SILVA W A. Reduced-order modeling：New approaches for computational physics［J］. Progress in Aerospace Sciences， 2004， 40（1-2）： 51-117. |
| 23 | BERKOOZ G， HOLMES P， LUMLEY J L. The proper orthogonal decomposition in the analysis of turbulent flows［J］. Annual Review of Fluid Mechanics， 1993， 25： 539-575. |
| 24 | HALL K C， THOMAS J P， DOWELL E H. Proper orthogonal decomposition technique for transonic unsteady aerodynamic flows［J］. AIAA Journal， 2000， 38（10）： 1853-1862. |
| 25 | DOWELL E H， THOMAS J P， HALL K C. Transonic limit cycle oscillation analysis using reduced order aerodynamic models［J］. Journal of Fluids and Structures， 2004，19（1）： 17-27. |
| 26 | LUCIA D J， BERAN P S， KING P I. Reduced-order modeling of an elastic panel in transonic flow［J］. Journal of Aircraft， 2003， 40（2）： 338-347. |
| 27 | MARKOVINOVI? R， JANSEN J D. Accelerating iterative solution methods using reduced-order models as solution predictors［J］. International Journal for Numerical Methods in Engineering， 2006， 68（5）： 525-541. |
| 28 | TROMEUR-DERVOUT D， Vassilevski Y. POD acceleration of fully implicit solver for unsteady nonlinear flows and its application on grid architecture［J］. Advances in Engineering Software， 2007， 38（5）： 301-311. |
| 29 | GRINBERG L， KARNIADAKIS G E. Extrapolation-based acceleration of iterative solvers： Application to simulation of 3D flows［J］. Communications in Computational Physics， 2011， 9（3）： 607-626. |
| 30 | RAPúN M L， VEGA J M. Reduced order models based on local POD plus Galerkin projection［J］. Journal of Computational Physics， 2010， 229（8）： 3046-3063. |
| 31 | CLAINCHE L S， VARAS F， Francisco J H V， et al. Accelerating oil reservoir simulations using POD on the fly［J］. International Journal for Numerical Methods in Engineering， 2017， 110（1）： 79-100. |
| 32 | TERRAGNI F， VALERO E， VEGA J M. Local POD plus Galerkin projection in the unsteady lid-driven cavity problem［J］. SIAM Journal on Scientific Computing， 2011，33（6）： 3538-3561. |
| 33 | RAPúN M L， TERRAGNI F， VEGA J M. Adaptive POD-based low-dimensional modeling supported by residual estimates［J］. International Journal for Numerical Methods in Engineering， 2015， 104（9）： 844-868. |
| 34 | TERRAGNI F， VEGA J M. Construction of bifurcation diagrams using POD on the fly［J］. SIAM Journal on Applied Dynamical Systems， 2014， 13（1）： 339-365. |
| 35 | BERGMANN M， BRUNEAU C H， IOLLO A. Enablers for robust POD models［J］. Journal of Computational Physics， 2009， 228（2）： 516-538. |
| 36 | BALAJEWICZ M， DOWELL E H. Stabilization of projection-based reduced order models of the Navier-Stokes［J］. Nonlinear Dynamics，2012， 70（2）： 1619-1632. |
/
| 〈 |
|
〉 |
CJA