Introduction - Computational River Dynamics - page 4

conditions in curved and braided channels and around river training works, bridge
piers, spur-dikes, and water intake structures.
Physical modeling and computational simulation are the two major tools used in
river engineering analysis. Both have their advantages and disadvantages. Physical
modeling can provide directly visible results, but it is expensive and time-consuming.
Because the flow, sediment transport, and bed change processes in rivers are very
complicated, it is difficult to ensure similarity between a physical model and its proto-
type. Errors may arise due to distortions of model scale and variations in experimental
environments such as temperature. Computational simulation gives direct, real-scale
predictions without any scale distortion and is cost-effective. However, the reliability
of computational simulation relies on how well the physical processes are mathemat-
ically described through governing equations, boundary conditions, and empirical
formulas; how accurately the differential governing equations are discretized using
numerical schemes; how effectively the discretized algebraic equations are solved using
direct or iterative solution methods; and whether the numerical solution procedures
are correctly coded using computer languages. If the mathematical description is unrea-
sonable, the numerical discretization incorrect, the solution method ineffective, or if
the computed code has bugs, the results from a numerical model cannot be trusted.
Because many empirical formulas are used to close the mathematical problems, the
applicability of computational simulation is still somehow limited. Before a numerical
model can be applied to a real-life project, it needs to be verified and validated using
analytical solutions and data measured in laboratories and fields.
To solve a real-life engineering problem correctly and effectively, the integration of
field investigation, physical modeling, and computational simulation is needed. Field
investigation is the first thing to do for a comprehensive understanding of the problem.
It provides the necessary hydrologic and sediment information on the study domain
and boundary conditions, which are required in both physical modeling and com-
putational simulation. It also provides data to calibrate physical and computational
models. If the study reach is not long, either physical modeling or computational sim-
ulation can be chosen to analyze the problem. The most cost-effective method is to use
physical models to study a few scenarios and collect enough data to calibrate compu-
tational models, and then use the calibrated computational models to analyze more
scenarios. If the study reach is too long, 1-D numerical models are often used in the
entire reach; they provide boundary conditions for 2-D and 3-D numerical models as
well as physical models for detailed analyses in important subreaches.
1.3 SCOPE, PROBLEMS, AND STRATEGIES
OF COMPUTATIONAL RIVER DYNAMICS
Computational river dynamics is a branch of computational fluid dynamics (CFD). It
solves river engineering problems using numerical methods. River flow is an incom-
pressible flow; therefore, many successful numerical methods developed in CFD can
be applied here. However, river flow has a free surface and movable bed, which make
computational river dynamics relatively complicated and difficult. Many assumptions
and empirical formulas must be used to close the mathematical systems, and the
approximate solutions sought may not be unique. Thus, computational river dynamics