minor

Author: hweifluids

source/3_numerical.rst

@@ -176,6 +176,10 @@ The continuous velocity field is reconstructed by trilinear interpolation of the
 
 
 
+**Tricubic by F. Lekien** ``I.P.``
+
+Marked as ``tricubicFL``, this variation of tricubic interpolator is still under development by the author.
+
 **Hermite**
 
 The ``hermite`` 
@@ -185,13 +189,10 @@ The ``hermite``
 The weighted essentially non-oscillatory ``WENO`` used here is a fifth-order WENO reconstruction (WENO-5). It is suggested to be used in research with intermittent capture need, e.g., high-speed flows and shock capture.
 It shows relatively poor performance in general cases, and comsuming more wall time. 
 The method originates from [Jiang1996]_ and expanded to three-dimensional computation, and [Shu2009]_ gave a review on the WEMO method.
-
 The process is given as follows.
 
-**Fifth-Order WENO Reconstruction (WENO-5)**
-
 The WENO-5 method reconstructs a non-oscillatory, fifth-order-accurate approximation of a function value at an arbitrary location :math:`x = x_{i+1/2} + t\,\Delta x`, where :math:`t \in [0,1)` and :math:`x_{i+1/2} = x_i + \tfrac{1}{2}\,\Delta x` on a uniform grid with :math:`\Delta x = 1`. 
-A five-point stencil ``{f_{i-2}``, ``f_{i-1}``, ``f_i``, ``f_{i+1}``, ``f_{i+2}}`` is used.
+A five-point stencil ``f_{i-2}``, ``f_{i-1}``, ``f_i``, ``f_{i+1}``, ``f_{i+2}`` is used.
 
 .. math::
 
@@ -266,7 +267,6 @@ Finally, reconstruct at :math:`x = x_{i+1/2} + t\,\Delta x` by combining:
 
    f_{\mathrm{WENO5}}(x_{i+1/2} + t\,\Delta x) = \omega_{0}\,p_{0}(t) + \omega_{1}\,p_{1}(t) + \omega_{2}\,p_{2}(t).
 
-The code computes :math:`t^{2}`, forms coefficients :math:`C_{\ell,k}`, evaluates :math:`p_{\ell}(t)`, computes :math:`\beta_{\ell}`, then :math:`\tilde{\alpha}_{\ell}`, :math:`\omega_{\ell}`, and returns :math:`\omega_{0}\,p_{0} + \omega_{1}\,p_{1} + \omega_{2}\,p_{2}` exactly as above.
 
 
 
@@ -305,6 +305,11 @@ Eigenvalue Solver
 ~~~~~~~~~~~~~~~~~~~~
 
 
+.. _numdyn:
+
+Windowing for Dynamic LCS
+----------------------------------------------
+
 
 
 .. _numcompare:

source/9_references.rst

@@ -12,10 +12,9 @@ Cited and Suggested by ``Py3DFTLE``
 
 .. [Butcher1964] Butcher J. C. "On Runge-Kutta processes of high order." *Journal of the Australian Mathematical Society* **4(2)** (1964). `link <https://doi.org/10.1017/S1446788700023387>`__
 
+.. [Jiang1996] G.-S. Jiang and C.-W. Shu. "Efficient Implementation of Weighted ENO Schemes." *Journal of Computational Physics* **126(1)** (1996). `link <https://doi.org/10.1006/jcph.1996.0130>`__
 
-.. [Jiang1996] G.-S. Jiang and C.-W. Shu. "Efficient Implementation of Weighted ENO Schemes." *Journal of Computational Physics* **126(1)** (1996). `link <https://doi.org/10.1006/jcph.1996.0045>`__
-
-.. [Shu2009] C.-W. Shu. "High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems." *SIAM Review* **51(1)** (2009). `link <https://doi.org/10.1137/080716034>`__
+.. [Shu2009] C.-W. Shu. "High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems." *SIAM Review* **51(1)** (2009). `link <https://doi.org/10.1137/070679065>`__