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adds working folder for unit test of forcing
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adds working folder for unit test of forcing
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adds working folder for unit test of forcing
Cristian Lalescu
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feature/forcing-unit-test
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Oct 7, 2024
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Forcing unit test
=================
For this test, velocity field is initialized as a single mode.
Numerical solution is compared with analytic solution for the different
available forcing methods.
**Linear forcing**
initial condition
.. math::
u(x,0) = U (e^{i\bar{k}\cdot x} + e^{-i\bar{k}\cdot x})
U \perp \bar{k}
solution
.. math::
u(x,t) = exp((-\nu\bar{k}^2 + \alpha)t) u(x,0)
where :math:`\alpha` is the linear coefficient.
**Fixed energy injection rate**
initial condition
.. math::
u(x,0) = U (e^{i\bar{k}\cdot x} + e^{-i\bar{k}\cdot x})
U \perp \bar{k}
solution has same form as for linear forcing, but
.. math::
U^2(t) = V^2 + (U^2(0) - V^2) exp(-2\nu\bar{k}^2 t)
with
.. math::
V^2 = \epsilon / (2\nu\bar{k}^2)
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