5.5 Spatial Order
5.5.1 Command Status
Optional - The commands in this section are only required if second order horizontal spatial reconstruction is specified, otherwise defaults will apply and the commands can be omitted from the .fvc file.
5.5.2 Description
Spatial order defines how the values of model variables, such as depth and velocity, are assigned at cell faces during calculation. First and second order options are available. The option to use is dependent on the modelling problem being investigated (See Appendix B.4.2). Supported spatial order model implementations are summarised in Table 5.6, with links to the relevant implementation sections below. Horizontal spatial order commands relevant to the 2D HD simulation class are provided in Table 5.7.
| Model Implementation | Description |
|---|---|
| First Order | Uses a first order numerical method when calculating fluxes between cells. |
| Second Order | Uses a second order numerical method when calculating fluxes between cells. |
| Command | Description |
|---|---|
| Spatial Order | Optional - Sets the horizontal spatial reconstruction to first or second order. |
| Horizontal Gradient Limiter | Optional - Sets the horizontal gradient limiter model used with second order horizonal spatial reconstruction. Ignored if using first order spatial reconstruction. |
| Horizontal AlphaR | Optional - Sets a reduction factor to scale between first and second order horizontal spatial reconstructions for depth, velocity and scalar model variable fields. Ignored if using first order spatial reconstruction. |
5.5.3 First Order
First order horizontal spatial reconstruction calculates fluxes between cells using a uniform value within each cell which provides a stable and reliable solution. It is the default spatial order implementation.
5.5.4 Second Order
Second order horizontal spatial reconstruction computes fluxes between cells using estimated gradients within each cell. This approach represents sub cell variation in flow properties rather than assuming uniform conditions and therefore produces a more accurate numerical solution. The scheme is typically applied to problems with strong spatial gradients in velocity or water level, such as those encountered in riverine channels and floodplain inundation modelling.