... | ... | @@ -428,15 +428,15 @@ criteria which are |
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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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*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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(*δU*) 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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(code parameter: `_C.amr_d1`) selects between a purely
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gradient-based criterion (*α* = 1) and a purely
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gradient-based criterion (*α*=1) and a purely
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second-derivatives-based criterion (*α* = 0).
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*U*<sub>*r**e**f*</sub> are reference values to avoid division by
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zero for indefinite variables. The exponent *ξ* ∈ \[0, 2\] (code
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parameter: `_C.amr_exp`) introduces a power law functional on the
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grid spacing ratio *δ* *x*<sup>(*l*)</sup>/*δ* *x*<sup>(0)</sup>
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grid spacing ratio *δx*<sup>(*l*)</sup>/*δx*<sup>(0)</sup>
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which allows to control the behavior with progressive mesh
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refinement. The macro `FILTER` (preset to 10<sup> − 2</sup>) is a
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filter to suppress refinement at small-scale solution wiggles. The
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... | ... | @@ -453,13 +453,11 @@ The criterion is applied to primary (or related) physical variables |
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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/f4f4b19589de242e49db03a088acdf8f/amr_Jeans.png)
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![amr_Jeans](uploads/88131f0e5135bb8e7b795ae51651b0bd/amr_Jeans.png)
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![amr_Jeans](uploads/7cc51d2e1126f09b32c9187ea6f87490/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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*δ* *s* = min {*δ* *x*, *h*<sub>*y*</sub>*δ* *y*, *h*<sub>*z*</sub>*δ* *z*}.
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*δs* = min {*δx*, *h*<sub>*y*</sub>*δy*, *h*<sub>*z*</sub>*δz*}.
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ℰ<sub>*J**e**a**n**s*</sub> is a user-specific threshold with the
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reciprocal value giving the minimum number of grid cells the local
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Jeans length should be resolved.
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