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

作者：Singer Michael A^*; Green William H

来源：Applied Numerical Mathematics, 2009, 59(2): 272-279.

DOI：10.1016/j.apnum.2008.02.004

• Model reduction
• Premixed flame
• Proper orthogonal decomposition
• Strang splitting

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(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.

• 出版日期2009-2