6.2 Spatial Order

6.2.1 Command Status

Optional - The commands in this section are only required if second order vertical spatial reconstruction is specified, otherwise defaults will apply and the commands can be omitted from the .fvc file.

6.2.2 Description

This section describes spatial order commands relating to vertical processes. Prior to reading this section users should review horizontal spatial order as described in the 2D HD Simulation Class Chapter (see Section 5.5.2). As for the 2D HD Simulation Class, first and second order vertical spatial order options are available. Supported vertical spatial order model implementations are summarised in Table 6.1, with links to the relevant implementation sections below. Vertical spatial order commands relevant to the 3D HD simulation class are provided in Table 6.2.

Table 6.1: Vertical 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 6.2: Vertical Spatial Order Commands
Command Description
Spatial Order Optional - Sets the vertical spatial reconstruction to first or second order.
Vertical Gradient Limiter Optional - Sets the vertical gradient limiter model used with second order vertical spatial reconstruction. Not used for first order vertical spatial construction.
Vertical AlphaR Optional - Sets a reduction factor to scale between first and second order vertical spatial reconstructions for vertical velocity model variable fields. Not used for first order vertical spatial construction.

6.2.3 First Order

First order vertical spatial reconstruction calculates fluxes between 3D cells using a uniform value within each cell. This provides a stable and reliable solution. It is the default spatial order implementation.

! First Order Horizontal and Vertical Spatial Accuracy
Spatial Order == 1,1 ! {1 1st Order Horizontal} | 2 2nd Order Horizontal, {1 1st Order Vertical} | 2 2nd Order Vertical

6.2.4 Second Order

Second order vertical spatial reconstruction computes fluxes between 3D cells using estimated gradients within each cell. This approach represents sub cell variation in vertical fluxes rather than assuming uniform conditions and therefore produces a more accurate numerical solution. The scheme is typically applied to problems with strong vertical gradients in velocity or where 3D hydrodynamics will underpin the simulation of density stratification if the model is intended to be extended to AD simulation (see Chapter 7).

! Second Order Vertical Spatial Accuracy
Spatial Order == 1,2 ! {1 1st Order Horizontal} | 2 2nd Order Horizontal, {1 1st Order Vertical} | 2 2nd Order Vertical

! Second Order Vertical Spatial Accuracy With Gradient Limiters
Spatial Order == 1,2 ! {1 1st Order Horizontal} | 2 2nd Order Horizontal, {1 1st Order Vertical} | 2 2nd Order Vertical
Vertical Gradient Limiter == MC ! {MC} | MINMOD | SUPERBEE
Vertical AlphaR == 0.5, 0.5 ! {1.0} AlphaV (velocity), {1.0} AlphaS (scalars, ignored in the 2D HD simulation class)