We introduce a new graph compression algorithm for block construction, which extends the method by Ashcraft and requires one simple to use parameter.We describe an improved block factorization computation in the VBARMS method.We conduct a parallel performance study of the VBARMS method using parallel graph partitioning.We solve turbulent three-dimensional Navier-Stokes equations on large realistic unstructured meshes. The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li etźal. 200314 for solving general nonsymmetric linear systems. The parallel VBARMS solver can detect automatically exact or approximate dense structures in the linear system, and exploits this information to achieve improved reliability and increased throughput during the factorization. A novel graph compression algorithm is discussed that finds these approximate dense blocks structures and requires only one simple to use parameter. A complete study of the numerical and parallel performance of parallel VBARMS is presented for the analysis of large turbulent Navier-Stokes equations on a suite of three-dimensional test cases.