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1D River Solvers

Developed for over 40 years, Flood Modeller’s advanced steady and unsteady 1D river solvers have become some of the fastest and most robust solutions available. It makes them an ideal choice for a wide-range of engineering and environmental applications. The solvers have been subjected to extensive testing and benchmarking against observations, analytical solutions and other modelling software.

Key facts

  • Suited to modelling flows and levels in open channels, floodplains, reservoirs and estuaries

  • Undertake integrated catchment modelling by linking to the 1D urban or suite of 2D solvers

  • Trusted by users for being fast, reliable and providing robust solutions

  • Includes a comprehensive range of structures including gates, abstractions, weirs and pumps

  • Allows logical rules to be applied to the operation of different structures

  • Apply point and distributed boundary inflows/conditions

  • Independently tested and benchmarked by government agencies and academics

  • Relied upon by government agencies for flood forecasting

At the core of Flood Modeller are its industry-leading steady and unsteady 1D solvers. They are suited to subcritical, supercritical and transitional flow regimes to confidently apply them to applications, ranging from steep river flows to tidally influenced estuaries.


In addition to the full hydrodynamic solvers, Flood Modeller includes flood routing capabilities, including the Muskingum and Muskingum-Cunge methods, providing users with a simplified way to calculate downstream discharges.

The 1D solver provides a comprehensive range of hydraulic structures, including gates, abstractions, weirs and pumps. Structures can be operated using logical rules for applications such as controlling the gate opening of a sluice or turning a pump on or off. This gives Flood Modeller a much wider range of application when compared to other 1D modelling software.

Flow boundaries to the 1D river solver can be applied either as a point inflow/outflow or distributed inflow/outflow along a river reach using one of the hydrological boundary units or the flow time boundary unit. Water level boundaries can be defined using either a time series water level boundary unit or as an automatically generated flow-head relationship using the normal/critical depth boundary unit. Boundaries to the 1D river solver can also be from links to the 2D solver and the 1D urban solver. 

Steady-state solver

Direct steady-state and Pseudo-Timestepping methods enable you to optimise run-time and enhance model stability. 

In order to carry out unsteady simulations, an estimate of the initial conditions (flow and stage) are required at every model node. This is most often obtained by carrying out a steady-state simulation at the proposed start time.


The main steady-state solution is the Direct Method and is applicable to in-bank flow regimes. It is a fast and very accurate solution which requires very little initial data. It also incorporates an optional supercritical and transcritical flow solver which has the capability of modelling hydraulic jumps and supercritical flow accurately.

The Pseudo-Timestepping method uses a Preissmann 4-point scheme and is often used to develop initial conditions for unsteady runs or where flows are initially out of bank. These initial conditions are used for the steady state run, with the boundary conditions held constant for the time at which the solution is required. 

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Unsteady-state solver

Using the Preissmann implicit scheme to solve the equations for free surface flow, based on the Saint-Venant equations for flow in open channels, this solver improves model performance.

The unsteady-state solver uses the “box” finite difference operator, which allows long time steps to be used. These operators enable the differential equations describing channel flows to be transformed into a set of linear algebraic equations connecting the flows and depths at discrete locations or nodes along the channel.


These equations are inevitably a combination of empirical and theoretical equations, many of them non-linear. The non-linear equations are first linearised and the solution to the linear form of the problem is then found.

Upcoming courses

Online Course

9th - 11th July 2024

Introduction to 1D river modelling


Online Course

16th & 17th July 2024

Introduction to 2D modelling


Online Course

23rd & 24th July 2024

Advanced Flood Modeller


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