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Corrected surface-normal gradient scheme

∇f⊥Q=αQP−QN∣d∣⏟implicit+(n^−αd^) ∙ (∇Q)f⏟explicit correction \snGrad Q = \underbrace{\alpha \frac{Q_P - Q_N}{| \vec{d} |}}_{\mathrm{implicit}} + \underbrace{\left( \hat{\vec{n}} - \alpha \hat{\vec{d}} \right) \dprod \left( \grad Q \right)_f}_{\mathrm{explicit\ correction}}

where

α=1cos(θ) \alpha = \frac{1}{cos(\theta)}

Properties​

  • Central-difference snGrad scheme with non-orthogonal correction
  • delta coefficients given by: nonOrthDeltaCoeffs
  • explicit non-orthogonal correction

Usage​

The scheme is specified using:

snGradSchemes
{
    default         none;
    grad(U)         corrected;
}

Further information​

Source code