deploy: 318a2ae

Author: hweifluids

.doctrees/3_numerical.doctree

@@ -103,7 +103,7 @@
 \[\frac{d\mathbf{x}}{dt} = \sigma\,\mathbf{u}(\mathbf{x},t)\,,
 \mathbf{x}(t_n)=\mathbf{x}_n\,,\]</div>
 <p>where <span class="math notranslate nohighlight">\(\sigma = \pm1\)</span> selects forward or backward integration.
-During the time integration process, the algorithm frequently queries the flow velocity vector <span class="math notranslate nohighlight">\(\mathbf{v}(\mathbf{x},t)\)</span> at specific locations and moments with very high precision requirements.
+During the time integration process, the algorithm frequently queries the flow velocity vector <span class="math notranslate nohighlight">\(\mathbf{u}(\mathbf{x},t)\)</span> at specific locations and moments with very high precision requirements.
 However, since the data grid is inherently spatially discretized, high-order interpolation methods are required by the program to keep numerical stability and obtain a physically meaningful flow map.
 Furthermore, when querying the velocity, special wall treatment must be applied at the boundaries to avoid value discontinuities and to represent certain real physical conditions.</p>
 <section id="time-integration">

.doctrees/environment.pickle

@@ -18,7 +18,7 @@ To obtain this map, one must numerically integrate the underlying dynamical syst
    \mathbf{x}(t_n)=\mathbf{x}_n\,,  
 
 where :math:`\sigma = \pm1` selects forward or backward integration.
-During the time integration process, the algorithm frequently queries the flow velocity vector :math:`\mathbf{v}(\mathbf{x},t)` at specific locations and moments with very high precision requirements.
+During the time integration process, the algorithm frequently queries the flow velocity vector :math:`\mathbf{u}(\mathbf{x},t)` at specific locations and moments with very high precision requirements.
 However, since the data grid is inherently spatially discretized, high-order interpolation methods are required by the program to keep numerical stability and obtain a physically meaningful flow map.
 Furthermore, when querying the velocity, special wall treatment must be applied at the boundaries to avoid value discontinuities and to represent certain real physical conditions.