Computational Hydraulics: Elements of the Theory of Free Surface Flows [Kõva köide]

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.