Assessment of solutions of finite difference equations in fluid mechanics

An analysis of computed numerical solutions to the governing differential equations for fluid mechanics problems is presented in order to demonstrate that small residuals do not indicate accuracy. Two different approximations are carried out to solve simple linear algebraic equations, with results which indicate that residuals are not practicable for obtaining exact solutions. Conversion of the governing nonlinear differential equations into nonlinear algebraic equations through the Newton-Raphson method is suggested, with a possible penalty in computing time.