Abstract
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.
Original language | English (US) |
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Pages (from-to) | 119-137 |
Number of pages | 19 |
Journal | International Journal for Numerical Methods in Fluids |
Volume | 62 |
Issue number | 2 |
DOIs | |
State | Published - Jan 2010 |
Externally published | Yes |
Keywords
- Consistent Newton-Raphson
- Incompressible Navier-Stokes
- Schur complement
- Stabilized finite elements
- Three-dimensional flows
- Variational multiscale formulation
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics