Vectorial Field: Offline

Preparation

The structure of the case study folder is the following

>> ./Study_case
	>> /Folder_1  		
		>> /0
		>> ...
		>> /constant
		>> /system
			controlDict
			blockMeshDict
			...
			PODsolverDict  <--- Dictionary needed for the input parameters				
	>> /Folder_2

The PODsolverDict must be put inside ./Study_case/Folder_1/system/

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

Offline_parameters
{
	field      U;			<---- VectorialField on which POD is performed 
	accuracy   0.999;		<---- relative energy retained by the POD modes
	maxBasis   20;			<---- Max number of POD modes
	foldersList  ( 
			"Folder_1" 
			"Folder_2") ;	<---- List of folder names containig the snapshots
}

Usage

Inside ./Study_case/Folder_1 launch

VectorialPOD_Offline

To include folder “0” use

VectorialPOD_Offline -withZero

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

VectorialPOD_Offline -region <regionName>

Results

POD basis all the other .txt files are saved in a separate folder called POD_(fieldName), which has the classical OpenFOAM structure.

>> ./Study_case
	>> /Folder_1  				 		
	>> /Folder_2		
	>> /POD_U		
		>> /0		        
			UPOD0
			UPOD1
			UPOD2
			...
							
		>> /constant				
		>> /system	
		>> /U_POD_Offline_files
			UEigenValues.txt  <---- POD generalised Eigenvalued
			UalphaCoeffs.txt  <---- POD expansion coefficients to be used for mapping in the POD-I
			UL2AbsError.txt   <---- Absolute error in L2
			UL2RelError.txt   <---- Relative error in L2

The absolute and relative error are computed as

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