A variational multiscale Newton-Schur approach for the incompressible Navier-Stokes equations

作者：Turner D Z^*; Nakshatrala K B; Hjelmstad K D

来源：International Journal for Numerical Methods in Fluids, 2010, 62(2): 119-137.

DOI：10.1002/fld.2014

• incompressible Navier-Stokes
• stabilized finite elements
• variational multiscale formulation
• consistent Newton-Raphson
• Schur complement
• three-dimensional flows

In the following paper, we present a consistent Newton-Schur (NS) solution approach for variational multiscale formulations of the time-dependent Navier-Stokes equations in three dimensions. The main contributions of this work are a systematic Study of the variational multiscale method for three-dimensional problems and an implementation of a consistent formulation suitable for large problems with high nonlinearity, unstructured meshes, and non-symmetric matrices. In addition to the quadratic convergence characteristics of a Newton-Raphson-based scheme, the NS approach increases computational efficiency and parallel scalability by implementing the tangent stiffness matrix in Schur complement form. As a result, more computations are performed at the element level. Using a variational multiscale framework, we construct a two-level approach to stabilizing the incompressible Navier-Stokes equations based on a coarse and fine-scale subproblem. We then derive the Schur complement form of the consistent tangent matrix. We demonstrate the performance of the method for a number of three-dimensional problems for Reynolds number up to 1000 including steady and time-dependent flows.

• 出版日期2010-1-20