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Update 3_numerical.rst
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source/3_numerical.rst

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@@ -18,7 +18,7 @@ To obtain this map, one must numerically integrate the underlying dynamical syst
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\mathbf{x}(t_n)=\mathbf{x}_n\,,
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where :math:`\sigma = \pm1` selects forward or backward integration.
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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.
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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.
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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.
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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.
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