`total`

definition

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module: IndisputableMonolith.NavierStokes.DiscreteVorticity
domain: NavierStokes
line: 32 · github
papers citing: none yet

open explainer

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open lean source

IndisputableMonolith.NavierStokes.DiscreteVorticity on GitHub at line 32.

browse module

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explainer page

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open explainer

depends on

used by

formal source

  29  omega : Fin siteCount → ℝ
  30
  31/-- Sum of a scalar field over the finite lattice window. -/
  32def total {siteCount : ℕ} (f : Fin siteCount → ℝ) : ℝ :=
  33  ∑ i : Fin siteCount, f i
  34
  35/-- RMS square of a scalar field. -/
  36def rmsSq {siteCount : ℕ} (f : Fin siteCount → ℝ) : ℝ :=
  37  total (fun i => (f i) ^ 2) / siteCount
  38
  39/-- RMS amplitude of a scalar field. -/
  40def rms {siteCount : ℕ} (f : Fin siteCount → ℝ) : ℝ :=
  41  Real.sqrt (rmsSq f)
  42
  43/-- Pointwise normalized amplitude relative to the RMS scale. -/
  44def normalizedAmplitude {siteCount : ℕ} (f : Fin siteCount → ℝ) (i : Fin siteCount) : ℝ :=
  45  |f i| / rms f
  46
  47/-- The total J-cost of a discrete vorticity field relative to its RMS scale. -/
  48def totalJcost {siteCount : ℕ} (f : Fin siteCount → ℝ) : ℝ :=
  49  total (fun i => Jcost (normalizedAmplitude f i))
  50
  51/-- Contribution fields appearing in the J-cost derivative identity. -/
  52structure ContributionFields (siteCount : ℕ) where
  53  transport : Fin siteCount → ℝ
  54  viscous : Fin siteCount → ℝ
  55  stretching : Fin siteCount → ℝ
  56
  57/-- Total contributions of the three pieces. -/
  58def totalTransport {siteCount : ℕ} (c : ContributionFields siteCount) : ℝ :=
  59  total c.transport
  60
  61def totalViscous {siteCount : ℕ} (c : ContributionFields siteCount) : ℝ :=
  62  total c.viscous

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