COMP_GradtEtaGrad_Version

define the way of numerically modeling the diffusion operator

defines the way how to numerically model the diffusion term \( \nabla^T \cdot \left( \eta \nabla \right)\) with \( \eta\) being any physical property such as viscosity, heat conductivity, etc. This will be important if the physical property has jumps or steep gradients. Default: COMP_GradtEtaGrad_Version = %GradtEtaGrad_Identity% Possible options:
  1. %GradtEtaGrad_DirectApproximation% :: estbalish the numerical operator by direct least-squares approximation under stability optimization, i.e. utmost diagonal dominance (takes additional computation time)
  2. %GradtEtaGrad_Identity% :: using the identity \( \nabla^T \cdot \left( \eta \nabla \right) = \nabla \eta^T \cdot \nabla + \eta \Delta\) and employ the already existing operators for Gradient and Laplacian
  3. %GradtEtaGrad_None% :: #only for testing, as it is mathematically wrong: establish simply set \( \nabla^T \cdot \left( \eta \nabla \right) = \eta \Delta\) and use the already computed Laplacian operator
  4. %GradtEtaGrad_DerivedOperator% derives the diffusion operator from the discrete laplace operator
This item is referenced in:
COMP_GradtEtaGrad_Version define the way of numerically modeling the diffusion operator