Numerical modelling (1D, 2D, 3D)

Rivers are complex components of the natural landscape. Originating as small streams at higher elevations, they flow downhill under the force of gravity, eventually discharging into the sea. Along this journey, a wide range of factors—including climate, sediment type, bank vegetation, bed slope, and discharge—evolve progressively. Seasonal elements such as river ice, ice jams, and fish migration periods further contribute to this complexity.

In addition to natural influences, rivers are also shaped by human interventions. Structures such as dams, culverts, bridges, pumping stations, and wastewater treatment plants—as well as both agricultural and municipal effluents—can alter flow patterns and modify a river’s physicochemical composition, often with undesirable consequences.

Given the complexity and interdependence of river processes, specific fluvial issues — such as problematic erosion at river bends — cannot be assessed in isolation. For instance, a solution designed to reduce erosion may inadvertently affect ice dynamics, sediment deposition, or flooding elsewhere along the system.

When applied by experienced hydraulic engineers, numerical hydrodynamic modeling serves as a powerful diagnostic tool to investigate the root causes of a client’s problem. The insights gained can then guide the development of solutions that reflect the complexity and holistic behavior of river systems. These solutions can be refined and tested directly within the model, allowing potential issues to be identified and addressed before the solution is put into place.

At Avizo, we have the expertise to address a wide range of hydrodynamic modeling challenges. Depending on the complexity of the problem and the specific requirements of each project, our experts work closely with clients to determine the most accurate and effective modeling approach. The table below outlines the types of applications best suited to 1D, 2D, and 3D numerical models.

For more details on the modeling approaches we offer at each level of complexity, please refer to the links provided below.

• One-Dimensional Hydraulic Modeling (HEC-RAS, River1D, FishXing)
• Two-Dimensional Hydraulic Modeling (HEC-RAS 2D, Telemac2D, SRH-2D, Delft3D)
• Three-Dimensional Hydraulic Modeling

One-Dimensional Hydraulic Modeling (HEC-RAS, River1D, FishXing)

One-dimensional (1D) hydraulic models provide cross-sectional average values for key hydrodynamic parameters such as water depth, velocity, bed shear stress, and water surface elevation. As the most widely used modeling approach historically, 1D models remain an excellent option for applications concerned primarily with water levels, flow depths, and general flow behavior.

These models are especially well-suited for assessing how engineered structures—such as culverts, bridges, dams, and weirs—affect water levels and bulk flow characteristics. Specialized 1D tools also exist for simulating river ice processes, including frazil ice production and transport, ice cover formation, and the impact of river ice on flow resistance and flood levels. Additionally, numerical tools like FishXing allow for the refinement of culvert designs to accommodate fish passage, enabling Avizo to tailor solutions that respect the biological limitations of specific target species (e.g. swimming speed thresholds and endurance).

Typical capabilities of 1D hydraulic models:

• Estimation of water surface elevations, average flow depths, velocities, and cross-sectional bed shear stress
• Simulation under both:
  • Steady flow conditions (constant discharge over time)
  • Unsteady flow conditions (time-varying discharge, i.e. hydrographs)
• Evaluation of the hydraulic impacts of bridges, culverts, weirs, and other infrastructure
• Simulation of the influence of ice covers on river hydraulics
• Analysis of the impact of ice jams on flood levels
• Floodplain and flood level estimation under suitable conditions
• Estimation of bulk sediment transport rates and assessment of sedimentation issues

1D models remain a cost-effective and reliable option for many common engineering problems and regulatory assessments.

Two-Dimensional Hydraulic Modeling (HEC-RAS 2D, Telemac2D, SRH-2D, Delft3D)

With the increasing availability of powerful commercial computing resources and high-resolution topo-bathymetric data from aerial LiDAR and bathymetric surveys, two-dimensional (2D) hydrodynamic modeling is rapidly becoming standard practice. Compared to 1D models, 2D models offer greater spatial resolution and provide more accurate predictions of depth, velocity fields, and bed shear stress across the river or floodplain domain.

Recent advancements in modeling software—such as the BASEMESH plugin for QGIS (Telemac) and the forthcoming HEC-RAS 2025 release—have further reduced the time and effort required to develop 2D models. In many cases, clients can now benefit from the increased accuracy of 2D modeling at a cost and turnaround time on par to that of 1D modeling.

2D hydraulic models are particularly well suited for applications where spatial variability in the flow field is important or where the interaction between flow and bathymetric features must be captured in detail.

Typical applications of 2D hydraulic models:

• Simulating open-water flood scenarios under current and future climate conditions
• Providing spatially distributed estimates of flow depth, velocity, and bed shear stress to support hydro-geomorphological analyses
• Studying sediment transport processes, including both bed load and suspended load dynamics
• Assessing the effects of river restoration projects on aquatic habitat quality for fish and other species
• Analyzing contaminant mixing in rivers, lakes, and estuaries, including:
  • Suspended sediment
  • Nutrient loading (e.g. phosphorus, nitrogen from agricultural runoff, fertilizers, and wastewater)
  • Thermal effluents and temperature-driven stratification
• Understanding wind-driven flow and mixing patterns in lakes and estuarine environments

2D modeling represents a balanced approach for many clients with applications requiring greater spatial accuracy, but who do not require an understanding of how the flow changes over depth.

Three-Dimensional Hydraulic Modeling

Three-dimensional (3D) hydraulic modeling provides the most detailed and accurate representation of flow dynamics in rivers, lakes, and engineered hydraulic systems. Unlike 1D and 2D models, 3D models resolve the flow field not only along the longitudinal and lateral directions but also vertically, allowing for the simulation of vertical velocity gradients, density-driven stratification, and recirculation phenomena. This makes 3D models particularly suitable for studying complex flow environments where buoyancy effects, turbulence, and vertical mixing play an important role.

There are two principal approaches to 3D hydrodynamic modeling, each suited to different levels of complexity and project needs:

Simplified layered 3D Modeling

In this approach, the water column is divided into a modest number of vertical layers (typically 3 to 10), allowing the model to capture key three-dimensional characteristics without incurring prohibitive computational costs. This method offers a valuable middle ground between 2D and full 3D (see below) models and is ideal for fluvial systems where vertical flow structures are important but complete vertical resolution is not required.

Typical applications suitable to simplified 3D modelling (Telemac3D, Delft3D):

• Modeling hydrogeomorphology and secondary flow structures in river bends
• Investigating stratification in rivers, lakes, and estuaries due to temperature or salinity gradients
• Simulating nearshore or coastal wave–current interactions
• Assessing contaminant transport and vertical mixing
• Evaluating scour potential around bridge piers and other infrastructure

Advanced 3D Computational Fluid Dynamics (CFD – OpenFOAM)

This more detailed approach involves discretizing the flow domain into many vertical layers and resolving the full set of three-dimensional, time-dependent flow equations. CFD models are capable of simulating complex, transient flow environments with high accuracy, making them ideal for diagnosing and optimizing the performance of hydrotechnical structures.

Avizo’s CFD Services Include:

• Analyzing flow behavior in and around fishways, spillways, wastewater treatment facilities, mixing chambers, and coastal protection structures
• Recirculation regions and flow separation
• Air entrainment (i.e. bubbles) and cavitation
• Buoyancy-driven circulation due to thermal or saline density gradients (e.g., thermal refuges for cold-water species such as Atlantic salmon)
• Predicting 3D velocity, pressure, and turbulence distributions
• Evaluating hydrodynamic forces acting on structural components
• Simulating pollutant dispersion and mixing dynamics with high fidelity
• Modeling buoyancy-driven flow phenomena
• Producing high-quality visualizations and animations for stakeholder presentations, reports, and public outreach