This paper presents efficient parallel methods for solving ill-conditioned linear systems arising in fluid dynamics problems. The first method is based on the Modified LU decomposition, applied as a preconditioner to the Conjugate gradient algorithm. Parallelization of this method is based on the use of nested twisted factorization. Another method is based on a highly parallel Algebraic multigrid algorithm with a new smoother developed for anisotropic grids. Performance comparisons demonstrate superiority of new methods over commonly used variants of the Conjugate gradient method.