Gamma dot documentation in TeX
@@ -309,13 +309,27 @@ class Aerogrid(object):
@staticmethod
def compute_gamma_dot(dt, tstep, previous_tsteps):
"""
- Computes the temporal derivative of gamma using finite differences.
+ Computes the temporal derivative of circulation (gamma) using finite differences.
+
It will use a first order approximation for the first evaluation
- (when len(previous_tsteps) == 1), and then second order ones.
- :param dt: delta time for the finite differences
- :param tstep: tstep at time n (current)
- :param previous_tsteps: previous tstep structure in order: [n-..., n-2, n-1]
- :return:
+ (when ``len(previous_tsteps) == 1``), and then second order ones.
+
+ .. math:: \\left.\\frac{d\\Gamma}{dt}\\right|^n \\approx \\lim_{\Delta t \\rightarrow 0}\\frac{\\Gamma^n-\\Gamma^{n-1}}{\\Delta t}
+
+ For the second time step and onwards, the following second order approximation is used:
+
+ .. math:: \\left.\\frac{d\\Gamma}{dt}\\right|^n \\approx \\lim_{\Delta t \\rightarrow 0}\\frac{3\\Gamma^n -4\\Gamma^{n-1}+\\Gamma^{n-2}}{2\Delta t}
+
+ Args:
+ dt (float): delta time for the finite differences
+ tstep (AeroTimeStepInfo): tstep at time n (current)
+ previous_tsteps (list(AeroTimeStepInfo)): previous tstep structure in order: ``[n-N,..., n-2, n-1]``
+
+ Returns:
+ float: first derivative of circulation with respect to time
+
+ See Also:
+ .. py:class:: sharpy.utils.datastructures.AeroTimeStepInfo
"""
if len(previous_tsteps) == 0:
