Geoscience Reference
In-Depth Information
is an engineering science rather than applied mathematics. Not only must a successful
numerical modeler possess knowledge about numerical techniques, but he or she must
also have enough experience in river engineering.
In computational river dynamics, the flow, sediment transport, and morphological
change processes in rivers are described by a set of coupled, non-linear algebraic and
differential equations that usually cannot be solved in closed form. The analysis of
river morphodynamic phenomena thus requires an approximation process, the end
result of which is a field of discrete property values at a finite number of locations
(“points” or “nodes”) distributed over the study domain. The general procedure for
developing a computational model consists, essentially, of the following steps:
(1) Conceptualize the complicated physical phenomena of study, with the necessary
simplifications and assumptions that express our understanding of the nature
of the system and its behavior (e.g., dimensionality; steady, quasi-steady, or
unsteady; laminar or turbulent; subcritical, supercritical, or mixed; gradually
or rapidly varied flow; fixed or movable bed; bed load, suspended load, or total
load; low or high sediment concentration; uniform or multiple sediment sizes;
equilibrium or non-equilibrium transport; cohesive or non-cohesive; bank ero-
sion; channel meandering; contaminants; solution domain; initial and boundary
conditions);
(2) Describe the physical phenomena of study using a set of algebraic and differential
equations that are subject to the conservation laws of mass, momentum, and
energy;
(3) Divide the study domain into a mesh of points, finite volumes, or finite elements
corresponding to the used numerical methods;
(4) Discretize the differential equations to equivalent algebraic equations by introduc-
ing 'trial functions', held to approximate the exact solution locally;
(5) Solve the coupled algebraic equations, which are subject to case-specific boundary
conditions, using an iteration or elimination algorithm to find the property values
at the grid points, and
(6) Code the established solution procedures using computer languages, such as
FORTRAN, C, or C++, and package the model with a graphical user interface for
pre- and post-processing, if possible.
The major problems in computational river dynamics include:
(1) Adequacy of the (simplified) conceptual models representing the complicated real
system and its behavior;
(2) Realism of the mathematical models describing the complex hydrodynamic and
morphodynamic processes that cannot be represented exactly (e.g., turbulence,
bed roughness, and the interaction between flow and sediment), and reliability of
the empirical formulas used to close the mathematical systems;
(3) Ability to generate adequate meshes over complex domains;
(4) Accuracy and consistency of numerical approximations;
(5) Numerical stability and computational efficiency of solution methods;
(6) Correctness of computer coding, and
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