ABSTRACT
This chapter considers finite element processes for BVPs described by non-linear differential operators. These BVPs could contain single or multi-dependent variables and could be in single or multi-dimensional spaces. The steady state 1D Burgers equation represents one dimensional form of momentum equation in viscous flows. The chapter considers example problems that require numerical simulation of two-dimensional Navier-Stokes equations for isothermal, incompressible, Newtonian fluids. This chapter shows that the theoretical solution of the approximate mathematical model underestimates pressure distribution but overestimates the shear stress when compared with the converged solution of the actual Navier-Stokes equations without approximation presented. It considers flow of compressible fluid over a stationary impermeable plate at various mach numbers. Numerical solutions of a variety of model problems in R1 and R2 containing nonlinear differential operators have been considered. It has been shown in chapter 3 that for such operators, all methods of approximations leading to integral forms yield VIC integral forms.
