Lines Matching refs:D

22 The function $\langle \phi \rangle (x,y)$ is represented on a 2-D finite element grid, taken from t…
141 These quantities have agreed-upon definitions for 1D, but in multiple dimensions their definitions …
175 \overline{\phi} - \nabla \cdot (\beta (\bm{D}\bm{\Delta})^2 \nabla \overline{\phi} ) = \phi
178 …tric positive-definite rank 2 tensor defining the width of the filter, $\bm{D}$ is the filter widt…
182 \int_\Omega \left( v \overline \phi + \beta \nabla v \cdot (\bm{D}\bm{\Delta})^2 \nabla \overline \…
183 - \cancel{\int_{\partial \Omega} \beta v \nabla \overline \phi \cdot (\bm{D}\bm{\Delta})^2 \bm{\hat…
187 The boundary integral resulting from integration-by-parts is crossed out, as we assume that $(\bm{D…
211 ### Filter Width Scaling Tensor, $\bm{D}$
214 The definition for $\bm{D}$ then becomes
217 \bm{D} =
225 In the case of $\bm{\Delta}$ being defined as homogenous, $\bm{D}\bm{\Delta}$ means that $\bm{D}$ e…
242 Under these assumptions, $\bm{D}$ then becomes:
245 \bm{D} =
254 While we define $\bm{D}\bm{\Delta}$ to be of a certain physical filter width, the actual width of t…
386 Those scalar filter widths correspond to the scaling correspond to $\bm{D} = c \bm{I}$, where $c$ i…