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.

Table 5.6: Horizontal Spatial Order Model Implementations
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.
Table 5.7: Horizontal Spatial Order Commands
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.

! First Order Horizontal Spatial Accuracy
Spatial Order == 1,1 ! {1} 1st Order Horizontal | 2 2nd Order Horizontal, The second term is related to 3D so is not used for the 2D HD simulation class

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.

! Second Order Horizontal Spatial Accuracy
Spatial Order == 2,1 ! {1} 1st Order Horizontal | 2 2nd Order Horizontal, The second term is related to 3D so is not used for the 2D HD simulation class

! Second Order Horizontal Spatial Accuracy With Gradient Limiters
Spatial Order == 2,1 ! {1} 1st Order Horizontal | 2 2nd Order Horizontal, The second term is related to 3D so is not used for the 2D HD simulation class
Horizontal Gradient Limiter == LCD ! {LCD} | MLG
Horizontal AlphaR == 1.0, 1.0, 1.0 ! {1.0} AlphaH (depth), {1.0} AlphaV (velocity), {1.0} AlphaS (scalars, ignored in the 2D HD simulation class)