TABLE OF CONTENTS For drainage problems that require unsteady flow simulation, using the dynamic wave Eqs. (6.3) and (6.7) or Eqs. (6.2) and (6.6) or their lower hydraulic level approximations described in Sec. 6.3.3, numerical solutions are in order because no analytical solutions are known for these sets of partial differential equations except for a few simple cases with noninertia or kinematic wave approximations. Numerical solution of the unsteady flow equations involves discretization with space and time and specifying the initial and boundary conditions.
No analytical solutions are known for the Saint-Venant equations or the surcharged sewer flow equation. Therefore, these equations for sewer flows are solved numerically with appropriate initial and boundary conditions. The differential terms in the partial differential equations are approximated by finite differences of selected grid points on a space and time domain, a process known as discretization. Substitution of the finite differences into a partial differential equation transforms it into an algebraic equation. Thus, the original set of differential equations can be transformed into a set of finite difference algebraic equations for numerical solution.
Theoretically, the computational grid of space and time need not be rectangular. Neither do the space and time differences ? x and ? t need be kept constant. Nonetheless, it is usually easier for computer coding to keep ? x and ? t constant throughout a computation. For surcharge flow, Eq. (6.19)...
