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Title: Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation

Abstract

We introduce an adaptive POD method to reduce the computational cost of reacting flow simulations. The scheme is coupled with an operator-splitting algorithm to solve the reaction-diffusion equation. For the reaction sub-steps, locally valid basis vectors, obtained via POD and the method of snapshots, are used to project the minor species mass fractions onto a reduced dimensional space thereby decreasing the number of equations that govern combustion chemistry. The method is applied to a one-dimensional laminar premixed CH{sub 4}-air flame using GRImech 3.0; with errors less than 0:25%, a speed-up factor of 3:5 is observed. The speed-up results from fewer source term evaluations required to compute the Jacobian matrices.

Authors:
;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
946257
Report Number(s):
UCRL-JRNL-236975
TRN: US200903%%349
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
Applied Numerical Mathematics, vol. 59, N/A, February 1, 2009, pp. 272-279
Additional Journal Information:
Journal Volume: 59
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS; ALGORITHMS; CHEMISTRY; COMBUSTION; FLAMES; MATRICES; SOURCE TERMS; VECTORS

Citation Formats

Singer, M A, and Green, W H. Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation. United States: N. p., 2007. Web.
Singer, M A, & Green, W H. Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation. United States.
Singer, M A, and Green, W H. Mon . "Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation". United States. https://www.osti.gov/servlets/purl/946257.
@article{osti_946257,
title = {Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation},
author = {Singer, M A and Green, W H},
abstractNote = {We introduce an adaptive POD method to reduce the computational cost of reacting flow simulations. The scheme is coupled with an operator-splitting algorithm to solve the reaction-diffusion equation. For the reaction sub-steps, locally valid basis vectors, obtained via POD and the method of snapshots, are used to project the minor species mass fractions onto a reduced dimensional space thereby decreasing the number of equations that govern combustion chemistry. The method is applied to a one-dimensional laminar premixed CH{sub 4}-air flame using GRImech 3.0; with errors less than 0:25%, a speed-up factor of 3:5 is observed. The speed-up results from fewer source term evaluations required to compute the Jacobian matrices.},
doi = {},
journal = {Applied Numerical Mathematics, vol. 59, N/A, February 1, 2009, pp. 272-279},
number = ,
volume = 59,
place = {United States},
year = {2007},
month = {12}
}