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Publication 03-CNA-06
Convergence of Numerical Approximations of the
Incompressible Navier Stokes Equations with Variable
Density and Viscosity Chun Liu and Noel J. Walkington 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 u nique, 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 |