Computational Hydraulics

Part 1 Discrete forms of conservation laws: fundamental laws; conservation laws and equation - mass, momentum, energy; Gailiean frames; mass, momentum and energy levels in relation to mass, momentum and energy flux densities; some worked examples. Part 2 Continuous forms of conservation laws: one-dimensional primitive forms for vertically homogeneous fluids; introduction of lateral inflows, bed slopes and resistance and driving stresses; expansions and contractions in one-dimensional flows; two-dimensional conservation forms for homogeneous fluids; one-dimensional flows in a stratfield fluid; Eulerian forms and algorithmic forms; Eulerian forms of Boussinesq equations. Part 3 The method of characteristics: the role of the method of characteristics in computational hydraulics; characteristics and invariants; regions of state; formation and computation of the hydraulic jump; indeterminacy conditions for the method of characteristics; further worked examples; uni-directional wave propagation; the linearized method of characteristics - uni-directional waves; the linearized method of characteristics - periodic waves; the characteristic varieties for two-dimensional nearly horizontal flows. Part 4 Numerical methods: the description problem - first remark; the three-point method of characteristics; the four-point method of characteristics; the description problem - second remark; introduction to direct difference methods using the example of the scalar wave equation; explicit difference methods for one-dimensional nearly horizontal flows; implicit difference methods for one-dimensional nearly horizontal flows; inverse difference methods for one-dimensional nearly horizontal flows; difference methods for one-dimensional flows of non-homogeneous fluids; difference methods for linearized two-dimensional nearly horizontal flows; difference methods for general two-dimensional nearly horizontal flows; an implicit difference method for a Boussinesq equation. Part 5 The foundations of computational hydraulics: introduction; historical background; weak solutions of systems of conservations laws; dissipative difference schemes; generalized difference forms of conservation laws; some elements of functional analysis; construction of weak solutions by filtering; applications of the energy norm; the description problem - third remark. Part 6 Applications of computational hydraulics: introduction; rig testing and field testing; examples of test rigs; examples of field tests; production models.