... | ... | @@ -426,8 +426,7 @@ criteria which are |
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- derivatives-based (most important in practice):
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![amr_deriv](uploads/25c608e1a335aca4242b34afb9e4ffeb/amr_deriv.png)
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The criterion is applied to primary (or related) physical variables
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The criterion is applied to primary (or related) physical variables
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*U* ( = {𝜚, **m**, *e*, **B**, *C*<sub>*c*</sub>}). Undivided first
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(*δ* *U*) and second (*δ* <sup>2</sup>*U*) differences are
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computed along various spatial directions. The switch *α* ∈ \[0, 1\]
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... | ... | @@ -454,7 +453,7 @@ criteria which are |
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flow features right in time.*
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- Jeans-length-based (important in simulations involving selfgravity):
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![amr_Jeans](uploads/6f5d6baa55c30a2a3ce4c5a11cca7cb3/amr_Jeans.png)
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![amr_Jeans](uploads/911451541e1624ab997d1ecb6bae6ca3/amr_Jeans.png)
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where the first factor is the local Jeans length with
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*c*<sub>*s*</sub> the sound speed and *G* the gravitational
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constant, and where
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... | ... | @@ -465,12 +464,7 @@ criteria which are |
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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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![amr_Field](uploads/9a6e2ca5c64e5f849e12f8dc1db029f5/amr_Field.png)
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where the first factor is the Field length with *L*(𝜚, *T*) the
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density- and temperature-dependent heatloss function and *κ* the
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thermal conduction coefficient. ℰ<sub>*F**i**e**l**d*</sub> is a
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