Numerical solver | Maxwell | Half-moment | Maxw./Num. | Half/Num. | |
$\rho_{\infty}$ | -2.41561 | -1.59617 | -2.23425 | 33.9% | 7.5% |
$S_{\infty}$ | 1.71757 | 1.59617 | 1.68775 | 7.1% | 1.7% |
We consider a linearized kinetic BGK equation and the associated acoustic system on a network. Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network. This analysis leads to the consideration of a fixpoint problem involving the solutions of kinetic half-space problems. This work extends the procedure developed in [15], where coupling conditions for a simplified BGK model have been derived. Numerical comparisons between different coupling conditions confirm the accuracy of the proposed approximation.
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Figure 3. Kinetic equation and wave equation with coupling conditions given by the Maxwell/half-moment approach and by the equality of $ S $. $ \rho,q,S $ on edge $ 2 $ (left) and edge $ 3 $ (right) at time $ T = 1 $. The values at the nodes obtained from the coupling conditions are denoted by a cross
Table 1. Comparison of results with the different approximations
Numerical solver | Maxwell | Half-moment | Maxw./Num. | Half/Num. | |
$\rho_{\infty}$ | -2.41561 | -1.59617 | -2.23425 | 33.9% | 7.5% |
$S_{\infty}$ | 1.71757 | 1.59617 | 1.68775 | 7.1% | 1.7% |
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Node connecting three edges and orientation of the edges
Kinetic equation and half-moment approximation for different relations of
Kinetic equation and wave equation with coupling conditions given by the Maxwell/half-moment approach and by the equality of
Diamond network
Kinetic equation and wave equation with coupling conditions given by the Maxwell/half-moment approach and by the equality of