IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Liang Zhao
Clemson University
https://mthsc.clemson.edu/directory/view_person.py?person_id=438
Abstract

A nonlinear approach on solving Navier-Stokes equations in velocity-vorticity form

  • Feb. 17, 2018
  • 3:20 p.m.
  • LeConte 412

We consider steady incompressible flow using a new formulation of Navier-Stokes equations in which the vorticity is considered to be an independent variable. Correspondingly, an augmented Lagrangian based preconditioner is proposed for solving the derived linear system. We derive a residual-based error estimator to achieve accurate solutions using adaptive mesh refinement. Finally, we show numerical experiments to demonstrate the correctness of the proposed scheme. The implementation is parallelized and scalable to allow for high resolution, 3d computations, so this nonlinear solver can be easily extended to solve large realistic problems and implemented on super computers.

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