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Diffstat (limited to 'source/know/concept/material-derivative/index.md')
| -rw-r--r-- | source/know/concept/material-derivative/index.md | 20 |
1 files changed, 0 insertions, 20 deletions
diff --git a/source/know/concept/material-derivative/index.md b/source/know/concept/material-derivative/index.md index 7225053..d11287d 100644 --- a/source/know/concept/material-derivative/index.md +++ b/source/know/concept/material-derivative/index.md @@ -88,26 +88,6 @@ $$\begin{aligned} } \end{aligned}$$ -Where the advective term is to be evaluated in the following way in Cartesian coordinates: - -$$\begin{aligned} - (\va{v} \cdot \nabla) \va{U} - = - \begin{bmatrix} v_x \\ v_y \\ v_z \end{bmatrix} - \cdot - \begin{bmatrix} - \displaystyle\pdv{U_x}{x} & \displaystyle\pdv{U_x}{y} & \displaystyle\pdv{U_x}{z} \\ - \displaystyle\pdv{U_y}{x} & \displaystyle\pdv{U_y}{y} & \displaystyle\pdv{U_y}{z} \\ - \displaystyle\pdv{U_z}{x} & \displaystyle\pdv{U_z}{y} & \displaystyle\pdv{U_z}{z} - \end{bmatrix} - = - \begin{bmatrix} - v_x \displaystyle\pdv{U_x}{x} & v_y \displaystyle\pdv{U_x}{y} & v_z \displaystyle\pdv{U_x}{z} \\ - v_x \displaystyle\pdv{U_y}{x} & v_y \displaystyle\pdv{U_y}{y} & v_z \displaystyle\pdv{U_y}{z} \\ - v_x \displaystyle\pdv{U_z}{x} & v_y \displaystyle\pdv{U_z}{y} & v_z \displaystyle\pdv{U_z}{z} - \end{bmatrix} -\end{aligned}$$ - ## References |