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

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 CH4–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.