| ... | ... | @@ -195,7 +195,7 @@ in that list the next superblock is given by the 'next grid' operator |
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The list ends if the next grid pointer is a NULL pointer. The following
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image illustrates the linked list concept.
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{width=80%}
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Assuming a serial run for the moment, looping over all superblocks `g`
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of mesh refinement level $l$ (index `il`) is as simple as
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| ... | ... | @@ -405,15 +405,9 @@ individually selected by the user. The standard implementation covers |
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the following criteria:
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- derivatives-based (most important in practice):
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$$\left[\alpha\frac{|\delta U|}{|U|+U_\mathrm{ref}}+(1-\alpha)
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\frac{|\delta^2U|}{|\delta U|+{\rm FILTER}\cdot(|U|+U_\mathrm{ref})}\right]
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\left(\frac{\delta x^{(l)}}{\delta x^{(0)}}\right)^{\xi}
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\left\{\begin{array}{ll}
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>\mathcal{E}_{U} &\exists U \quad\hbox{refinement}\\
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<0.8\mathcal{E}_{U} & \forall U \quad\hbox{derefinement}\\
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\end{array}\right.$$
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{width=80%}
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The criterion is applied to physical variables $U$
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($=\{\varrho,\mathbf{m},e,\mathbf{B},C_\mathrm{c}\}$). Undivided
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first ($\delta U$) and second ($\delta^2U$) differences are computed along
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| ... | ... | @@ -438,13 +432,9 @@ the following criteria: |
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side) to decide whether a child block is to be created.
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- Jeans-length-based (important in simulations involving selfgravity):
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$\left(\frac{\pi}{G}\frac{c_s^2}{\varrho}\right)^{1/2}
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\cdot \mathcal{E}_\mathrm{Jeans}\left\{\begin{array}{ll}
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<\delta s & \mbox{refinement}\\
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>1.25\delta s & \mbox{derefinement}\\
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\end{array}\right.$
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{width=80%}
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where the first factor is the local Jeans
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length with $c_s$ the sound speed and $G$ the gravitational
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constant, and where $\delta s=\min\{\delta x,h_y\delta y, h_z\delta z\}$.
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| ... | ... | @@ -454,14 +444,9 @@ the following criteria: |
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- Field-length-based (potentially relevant for simulations involving a
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heatloss source but rarely used in practice):
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$$2\pi \left(\frac{\kappa T}{\max\left\{T\left(\frac{\partial L}{\partial T}\right)_{\varrho}
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-\varrho \left(\frac{\partial L}{\partial \varrho}\right)_{T},EPS\right\}}
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\right)^{1/2}\cdot \mathcal{E}_\mathrm{Field}\left\{\begin{array}{ll}
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<\delta s & \mbox{refinement}\\
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>1.25\delta s & \mbox{derefinement}\\
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\end{array}\right.$$
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{width=80%}
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where the first factor is the Field length with
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$L(\varrho, T)$ the density- and temperature-dependent heatloss
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function and $\kappa$ the thermal conduction coefficient.
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