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Title: ERROR ESTIMATES FOR A POD METHOD FOR SOLVING VISCOUS G-EQUATIONS IN INCOMPRESSIBLE CELLULAR FLOWS
The G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing regular solutions of viscous G-equations in incompressible steady and time-periodic cellular flows. Our method is based on the Galerkin proper orthogonal decomposition (POD) method. To facilitate the algorithm design and convergence analysis, we decompose the solution of the viscous G-equation into a mean-free part and a mean part, where their evolution equations can be derived accordingly. We construct the POD basis from the solution snapshots of the mean-free part. With the POD basis, we can efficiently solve the evolution equation for the mean-free part of the solution to the viscous G-equation. After we get the mean-free part of the solution, the mean of the solution can be recovered. We also provide rigorous convergence analysis for our method. Numerical results for viscous G-equations and curvature G-equations are presented to demonstrate the accuracy and efficiency of the proposed method. In addition, we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows.  more » « less
Award ID(s):
1854434
NSF-PAR ID:
10249390
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
SIAM journal on scientific computing
Volume:
43
Issue:
1
ISSN:
1064-8275
Page Range / eLocation ID:
A636-A662
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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