COMP_EtaGrad_Version
define the way of numerically modeling the property-times-gradient operator
defines the way how to numerically model terms of the form \( \eta \nabla u\) where \( \eta\) is a material property, that might have discontinuities.
Default:
COMP_EtaGrad_Version =
%EtaGrad_Classical%
Possible options:
-
- %EtaGrad_Classical% :: estbalish the numerical operator exactly as it is: \( \eta \nabla u = \eta_i \cdot \sum c^{\nabla}_{ij} u_j\)
- %EtaGrad_Identity% :: estbalish the numerical operator as:
\( \begin{array}{*{35}{l}} \eta \nabla u &= \eta \nabla (u-u_0) \\ &= \nabla \left( \eta (u-u_0) \right) - (u-u_0) \nabla \eta \\ &= \nabla \left( \eta (u-u_0) \right) \\ &= \sum c^{\nabla}_{ij} \left( \eta_j (u_j-u_i) \right) \end{array}\)
This option might improve the numerical solution if the material property has jumps.
This has impact, most of all, on the term \( \frac{1}{\rho} \nabla p\) occurring in the equation nof momentum, see
EquationsToSolve .