Using Adaptive Proper Orthogonal Decomposition to Solve the Reaction-Diffusion Equation

摘要

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.