Update 3_numerical.rst

Author: hweifluids

source/3_numerical.rst

@@ -3,5 +3,56 @@
 Numerical Methods
 ===================
 
+
+.. _wall:
+
+Wall Treatment
+~~~~~~~~~~~~~~~
+
+
+
+.. _advc:
+
+Lagrangian Advection
+~~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _intp:
+Velocity Interpolation
+~~~~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _grad:
+Gradient Discretization
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _eigen:
+Eigenvalue Solver
+~~~~~~~~~~~~~~~~~~~~
+
+
+
+
+.. _numcompare:
+
 Computational Density and Comparison
-==========================================
+==========================================
+
+.. _numtips:
+
+General Tips
+~~~~~~~~~~~~~~~~
+
+
+As for your reference, and configured as defaults, the *Berkeley LCS Tutorials* used ``RK4`` for advection.
+The velocity fields were interpolated with ``tricubic-FL`` by them, originating from [Lekien2005]_, which has higher performance by solving a 64*64 linear system using the function values, gradients, and mixed partial derivatives at its eight corners, which is in future development plan for ``Py3DFTLE`` with high priority.
+Although not detailed, ``grad_order=2`` was employed by them from the equation, supposing the mesh is sufficiently refined.
+
+Please always notice that, although providing much better numerical precision and looks cool in papers, high-order methods could be resource-consuming, even several hundred times.