DIFFOP_gradient
type of least squares approximation stencils for gradients
Default:
DIFFOP_gradient = DIFFOP_gradient_MLS
We have two options of expressing the coefficients for the gradient that consist of the coefficients of the derivatives in \( x\)-, \( y\)-, and \( z\)-direction:
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- Classical: \( c^\nabla_{ij} = \left(c^x_{ij}, c^y_{ij}, c^z_{ij}\right)\) which is the typical way of gradient/derivative approximation.
- Derived: \( c^\nabla_{ij} = \left( \frac{1}{2}c^\Delta_{ij}(x_j-x_i), \frac{1}{2}c^\Delta_{ij} (y_j-y_i), \frac{1}{2}c^\Delta_{ij} (z_j-z_i) \right)\) here, the laplace together with the distance terms is used. The order of approximation is usually one less than the approximation order of \( c^\Delta_{ij}\).
DIFFOP_gradient_MLS uses the classical computation of the coefficients. The derived coefficients can be used in the
ComputationOfPHI algorithm.