Publication 03-CNA-006

Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity

Chun Liu
Department of Mathematics
Pennsylvania State University
State College, PA 16802
liu@math.psu.edu

Noel J. Walkington
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
noelw@andrew.cmu.edu

Abstract: We consider numerical approximations of incompressible Newtonian fluids having variable, possibly disocntinuous, density and viscosity. Since solutions of the equations with variable density and viscosity may not be unique, numerical schemes may not converge. In two dimensions we show that if the solution is unique, then approximate solutions computed using the discontinuous Galerkin method to approximate the convection of the density and classical Taylor-Hood approximations ofthe momentum equation converge to the solution. If the solution is not unique a sub-sequence of these approximate solutions will converge to a solution.

Get the paper in its entirety as  03-CNA-006.pdf

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