Introduction
Computational Hydraulics is defined by Abbot and Minns (1998) as:
Mathematical Models
Classification of models is done in order to understand the type and level of mathematics involved in developing a model, and it helps understand how the simulation is done (Lane & Nichols, 1993). Model classification helps users select the appropriate model for a particular problem-solving need.
Model Types by Representation
- Lumped conceptual models represent water-related systems through global storage entities (e.g., surface water, aquifer storage) and follow principles like continuity, but lack a complete description of driving forces (e.g., rainfall-runoff models).
Model Type Classification
By system and representation
Water Engineering Problems
- Steady-state problems in hydraulics involve systems that do not change over time, and their equations exclude time as a variable.
The Modelling Cycle
Model building is a cycle rather than a one-shot process: the physical system (problem description) is translated into a mathematical formulation (mathematical model), which is discretized using a discretization strategy — the strong form (FDM), the weak form (FEM), or the finite volume approach (FVM) — to produce a discrete model and its numerical solution. The results are then visualized, which in turn feeds back into refining the understanding of the physical system.
Model Selection
- Model relevance: The model should address the problem effectively by representing the necessary processes, considering the equations used, and understanding the assumptions and limitations of the mathematical model.
Model Development Process
Developing a model follows a structured pipeline, from problem definition through to post-processing of results.