Using if loops or min/max functions

[nathan magnan]

Hello,

One of my substitutions links viscosity to temperature:

nu_func = lambda T: nu_max * np.tanh(np.exp(Nnu * (NT / T - 1)) / nu_max)

namespace[f'nu'] = nu_func(T)

The issue is that if Nnu * (NT / T - 1) is larger than 1000, the exponential overflows.

Physically, large value of  Nnu * (NT / T - 1 are irrelevant, since the tanh saturates as soon as Nnu * (NT / T - 1) is larger than 10.

Therefore, I would be completely with something like this

def nu_func(T):

    if (Nnu * (NT / T - 1) <= 10):

        return nu_max * np.tanh(np.exp(Nnu * (NT / T - 1)) / nu_max)

    else:

        return nu_max

But the if loop is rejected by dedalus, and I get the following error:

TypeError: operand type(s) all returned NotImplemented from __array_ufunc__(<ufunc 'less'>, '__call__', array(13.12236338), Mul(0.1, Add(Mul(2500001.0000000023, Pow(Add(Convert(Convert(<Field 127701709158352>)), Mul(2500000.0000000023, <Field 127701846261968>)), -1)), Convert(Convert(<Field 127701847398800>))))): 'ndarray', 'MultiplyNumberField'

I've tried the equivalent trick using the min function, but got a similar error.

What's the dedalus way to work around this?

Thanks for your help !

Nathan

[Daniel Lecoanet]

Hi Nathan,

You want to use a GeneralFunction. You can search the mailing list for more information about this.

Daniel

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[nathan magnan]

Hi Daniel,

Thanks for the swift answer !

I haven't tried yet, I'm gonna do that.

Though I'm worried I might run into the same issue as described in the thread "General function implentation in equation has no effect", because I'm also solving a NLBVP.

Best regards,

Nathan

[Daniel Lecoanet]

Hi Nathan,

The way that we solve NLBVPs is to linearize the equations and use Newton’s method to find a solution to the linearized problem. It is tricky to linearize an if statement. I would recommend you use a smoothed version of the if statement if you want to use an NLBVP. This way you would not need to use a GeneralFunction.

Daniel

To view this discussion visit https://groups.google.com/d/msgid/dedalus-users/0841c812-bee3-4b59-a708-6ed4ca79cd23n%40googlegroups.com.