Inadequacy of First - Order Upwind Difference Schemes for Some Recirculating Flows *

Spurious numerical solutions of problems with closed sub-characteristics by upwind difference schemes, in particular problems of recirculating incompressible flow at high Reynolds numbers, are proved to be due to the anisotropy of the artificial viscosity. Numerical examples are presented to show that even very simple problems, including basic problems in fluid dynamics, are not approximated well by schemes with anisotropic artificial viscosity, regardless of numerical parameters.