Page - 295 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

9.2 FiniteDifferenceMethods 295 Problemswith reusing therhs function Therhs functionmust takeuandtasarguments,because that is requiredby theode_FE function. What about the variablesbeta,dx,L,x,dsdt,g, and dudx that therhs function needs? These are global in the solution we have presented so far. Unfortunately, this has an undesired side effect: we cannot import therhs function in a new file, definedudx anddsdt in this new file and get the importedrhs to use these functions. The importedrhswill use theglobalvariables, includingfunctions, in itsownmodule. Howcanwefindsolutions to thisproblem?Technically,wemustpack the extra data beta, dx, L, x, dsdt, g, and dudxwith the rhs function, which requires more advanced programming considered beyond the scope of this text. A class is the simplest construction for packing a function together with data, see the beginning of Chapter 7 in [11] for a detailed example on how classes can be used in such a context. Another solution in Python, and especially in computer languages supporting functional programming, is so calledclosures.TheyarealsocoveredinChapter7 inthementionedreference and behave in a magic way. The third solution is to allow an arbitrary set of arguments forrhs in a list to be transferred toode_FEand then back torhs. AppendixH.4 in [11]explains the technicaldetails. 9.2.4 Animation:HeatConductioninaRod Let us return to the case with heat conduction in a rod (9.1)–(9.4). Assume that the rod is 50cm long and made of aluminum alloy 6082. Theβ parameter equals κ/( c), where κ is the heat conduction coefficient, is the density, and c is the heat capacity. We can find proper values for these physical quantities in the case of aluminum alloy 6082: = 2.7 · 103 kg/m3, κ = 200 WmK, c = 900 JKkg. This results in β = κ/( c) = 8.2 · 10−5 m2/s. Preliminary simulations show that we are close to a constant steady state temperature after 1h, i.e., T = 3600s. Therhs function from the previoussection can be reused, only the functionss, dsdt,g, anddudxmust bechanged(seefilerod_FE.py): def dudx(t): return 0 def s(t): return 323 def dsdt(t): return 0 def g(x, t): return 0