Two new approaches to the determination of constrained lumping schemes are presented. They are based on the property that the lumping schemes validated in the whole composition Yn-space of y are only determined by the invariance of the subspace spanned by the row vectors of lumping matrix M with respect to the transpose of the Jacobian matrix JT(y) for the kinetic equations. It is proved that, when a part of a lumping matrix MG is given, each row of the part of the lumping matrix to be determined, MD, is certain linear combinations of a set of eigenvectors of a special symmetric matrix. This symmetric matrix is related to MTG and AkMTG, where Ak are the basis matrices of JT (y). It is shown that the approximate lumping matrices containing MG with different row number n̂(n̂ < n) and global minimum errors can be determined by an optimization method. Using the concept of the minimal invariant subspace of a constant matrix over a given subspace one can directly obtain the lumping matrices containing MG with different n̂. The accuracy of these lumping matrices are shown to be satisfactory in sample calculations.
All Science Journal Classification (ASJC) codes
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering