4. Discretization of the Conservation Equations

Up to now, the conservation equations can only be solved analytically for special cases such as stationary one-dimensional flows. For more complex flows, they are solved approximately numerically. In the first two sections of this chapter, numerical solution methods for solving the conservation equations are presented. These convert the partial derivatives in the conservation equations into finite differences. Approximation errors of the methods are also discussed here. As a result of the numerical solution methods, a linear system of equations of difference equations is obtained whose matrices are sparse matrices. Solution methods for this are given in the third section. At the end of this chapter, the boundary conditions for flow problems are described.