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A variational multiscale Newton-Schur approach for the incompressible Navier-Stokes equations | | D. Z. Turner
; K. B. Nakshatrala
; K. D. Hjelmstad
; | | Date: |
28 Sep 2008 | | Abstract: | In the following paper, we present a consistent Newton-Schur 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 Newton-Schur 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. | | Source: | arXiv, 0809.4802 | | Services: | Forum | Review | PDF | Favorites | |
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