Abstract
The algorithms described in Chap. 7 are implemented in the C++ finite element code ParMooN (Wilbrandt et al., Comput Math Appl 74(1):74–88, 2017). In this chapter several examples from the literature are introduced and numerical results shown. To begin with, a more general discussion on numerical examples is given.
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Notes
- 1.
This is occasionally called direct numerical simulation (DNS).
- 2.
In fact it is also possible to have a right-hand side g ∈ L 2(Ω) in the equation ∇⋅u = g. While the saddle point theory covers this case as well, fluids are divergence-free and so examples are expected to respect this.
- 3.
- 4.
The surfaces sometimes intersect (especially for larger γ p and larger K) which is not correctly visible in the figure. However the presentation is clearer without these intersections.
- 5.
As a general similarity let a, b > 0. If γa + b < ε for some ε, then a < ε∕γ and b < ε. That means if a and b are equations and γ large, equation a is fulfilled with a higher accuracy compared with b.
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Wilbrandt, U. (2019). Numerical Results. In: Stokes–Darcy Equations. Advances in Mathematical Fluid Mechanics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-02904-3_8
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DOI: https://doi.org/10.1007/978-3-030-02904-3_8
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