A multi-level preconditioned iterative method based on a multi-level block ILU factorization preconditioning technique is introduced and is applied to the solution of unstructured sparse linear systems arising from the numerical simulation of coating problems. The coefficient matrices usually have several rows with zero diagonal values that may cause stability difficulty in standard ILU factorization techniques. The new preconditioning strategy employs a diagonal threshold tolerance and a local reordering of individual blocks to increase robustness of the multi-level block ILU factorization process.