Error estimates for a POD method for solving viscous Gequations in incompressible cellular flows
Abstract
The Gequation is a wellknown model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing \textcolor{black}{regular solutions} of viscous Gequations in incompressible steady and timeperiodic 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 Gequation into a meanfree part and a mean part, where their evolution equations can be derived accordingly. We construct the POD basis from the solution snapshots of the meanfree part. With the POD basis, we can efficiently solve the evolution equation for the meanfree part of the solution to the viscous Gequation. After we get the meanfree part of the solution, the mean of the solution can be recovered. We also provide rigorous convergence analysis for our method. Numerical results for \textcolor{black}{viscous Gequations and curvature Gequations} are presented to demonstrate the accuracy and efficiency of the proposed method. In addition, we study the turbulent flame speeds of the viscous Gequations in incompressible cellular flows.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 DOI:
 10.48550/arXiv.1812.09853
 arXiv:
 arXiv:1812.09853
 Bibcode:
 2018arXiv181209853G
 Keywords:

 Mathematics  Numerical Analysis;
 65M12;
 70H20;
 76F25;
 78M34;
 80A25
 EPrint:
 31 pages, 34 figures