Discrepancy between Navier-Stokes into and first example
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Assessment
- Difficulty
- 2/5
- Estimated time
- 1-3 hours
- Newbie friendliness
- 50/100
- Issue type
- Bug
- Clarity
- Clearly specified
- Activity status
- Stale
- Tech stack
- python
- Domain
- documentation
Research direction
Compare the Navier-Stokes introductory page at the equation-ipcs-one section with the first example problem at ns_code1.html, focusing on the definition of u^(n+1/2) and the shown F1 code. Confirm the intended intermediate variable, update the explanation or example so they agree, and verify that the equation and code describe the same scheme.
Written by the indexing model from the issue text.
Description
In the Navier-Stokes introductory page, an intermediate step is described here. By the definition of $u^{n+\frac12} = \frac12 (u^{n}+u^{n+1})$, the equation depends on $u^\ast$ as well as $u^{n+1}$. In the first example problem, it seems $u^\ast$ is implicitly assumed to be the same as $u^{n+1}$:
# previously
U = 0.5 * (u_n + u)
# ...
p_n = Function(Q)
p_n.name = "p_n"
F1 = rho * dot((u - u_n) / k, v) * dx # here
F1 += rho * dot(dot(u_n, nabla_grad(u_n)), v) * dx
F1 += inner(sigma(U, p_n), epsilon(v)) * dx
F1 += dot(p_n * n, v) * ds - dot(mu * nabla_grad(U) * n, v) * ds
F1 -= dot(f, v) * dx
a1 = form(lhs(F1))
L1 = form(rhs(F1))
I believe this discrepancy is resolved by instead defining:
$u^{n+\frac12} := \frac12 (u^{n}+u^{*})$
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