Vectorial Field: Online

To be used only after VectorialPOD_Offline: this solver implements a POD projection to vector fields.

Preparation

The structure of the case study folder is the following (in this example Folder3 and Folder4 are the test case folders)

>> ./Study_case
	>> /Folder_1  			
	>> /Folder_2
	>> /Folder_3  			
	>> /Folder_4		
	>> /POD_(fieldName)
		>> /0		        		
		>> /system		
			controlDict
			blockMeshDict
			...
			PODsolverDict  <--- Dictionary needed for the input parameters	
		>> /constant
		>> /(fieldName)_POD_Offline_files

The PODsolverDict must be put inside ./Study_case/POD_(fieldName)/system/

An example of PODsolverDict can be found in application/POD/VectorialPOD_Online, which requires the following entries:

Online_parameters
{
	field      U;			<---- ScalarField on which POD is performed 
	BasisNumber   20;		<---- number of POD modes to use
	foldersList  ( 
			"Folder_3" 
			"Folder_4" ) ;	<---- List of folder names containig the snapshots to be reconstructed
}

Usage

Inside ./Study_case/POD_(fieldName) launch

VectorialPOD_Online

To include folder “0” use

VectorialPOD_Online -withZero

To perform on a specified region (for multi-region cases) use

VectorialPOD_Online -region <regionName>

Results

The residual field is defined as the absolute difference between the test snapshot and the reconstruction and it is stored in the snapshot folder, as well.

>> ./Study_case
	>> /Folder_1  		  		
	>> /Folder_2
	>> /Folder_3
		>> /0
			UPODreconstruct  <--- U POD reconstruction obtained with BasisNumber basis
			UPODresidual     <--- U POD reconstruction obtained with BasisNumber basis
		>> /1	
			UPODreconstruct
			UPODresidual
		>>  ...			
				
	>> /Folder_4
		>> /0
			UPODreconstruct  <---(fieldName) POD reconstruction obtained with BasisNumber basis
			UPODresidual     <---(fieldName) POD reconstruction obtained with BasisNumber basis
		>> /1	
			UPODreconstruct
			UPODresidual
		>>  ...		
			
	>> /POD_U		
		>> /0		        				
		>> /system			
		>> /constant
		>> /U_POD_Offline_files
		>> /U_POD_Online_files
			maximum_L2_relative_error.txt <---- max L2 absolute error as a function of basis number
			average_L2_relative_error.txt <---- max L2 relative error as a function of basis number

The absolute and relative error are computed as

\[E_N^{L^2} = || \mathbf{u}-\mathbf{u}_{N}^{POD}||_{L^2}\qquad \epsilon_N^{L^2} = \frac{|| \mathbf{u}-\mathbf{u}_{N}^{POD}||_{L^2}}{|| \mathbf{u} ||_{L^2}}\]