adam_turbulence_library

ADAM, pointwise algebraic subgrid-scale models (issue #119, T1), shared by the CPU loops and the FNL device kernels.

Every routine returns the kinematic eddy viscosity nu_t from the velocity gradient g(a,b) = d u_a / d x_b, the constant c, the grid steps dl and the filter width delta. It is pure, takes explicit-size dummies and is tagged !$acc routine seq + !$omp declare target. The formulas come from the literature through the llm-wiki bundle turbulence-modelling; their constants were calibrated on other discretizations, not on WENO.

• Vreman (2004): nu_t = c sqrt(B / (a_ij a_ij)), a_ij = d u_j / d x_i, b_ij = sum_m dl_m^2 a_mi a_mj, B = b_11 b_22 - b_12^2 + b_11 b_33 - b_13^2 + b_22 b_33 - b_23^2; c = 2.5 C_s^2. Zero where a_ij has rank 1, pure shear among them.
• WALE (Nicoud & Ducros 1999): nu_t = (c delta)^2 (Sd:Sd)^(3/2) / ((S:S)^(5/2) + (Sd:Sd)^(5/4)), S the strain, Sd the traceless symmetric part of g g. Zero in pure shear.
• Sigma (Nicoud et al. 2011): nu_t = (c delta)^2 s_3 (s_1 - s_2) (s_2 - s_3) / s_1^2, s_i the singular values of g, from the invariants of g^T g in closed form. Zero in 2-D flow, pure shear and solid rotation.

Source: src/lib/common/adam_turbulence_library.F90

Contents

• sgs_vreman
• sgs_wale
• sgs_sigma

Subroutines

sgs_vreman

Vreman eddy viscosity.

Attributes: pure

subroutine sgs_vreman(c, dl, delta, g, nu)

Arguments

Name	Type	Intent	Attributes	Description
c	real(kind=R8P)	in		Model constant, 2.5 C_s^2.
dl	real(kind=R8P)	in		Grid steps.
delta	real(kind=R8P)	in		Filter width (unused: the model reads the steps).
g	real(kind=R8P)	in		Velocity gradient, g(a,b) = d u_a / d x_b.
nu	real(kind=R8P)	out		Eddy viscosity.

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sgs_wale

WALE eddy viscosity.

Attributes: pure

subroutine sgs_wale(c, dl, delta, g, nu)

Arguments

Name	Type	Intent	Attributes	Description
c	real(kind=R8P)	in		Model constant C_w.
dl	real(kind=R8P)	in		Grid steps (unused).
delta	real(kind=R8P)	in		Filter width.
g	real(kind=R8P)	in		Velocity gradient, g(a,b) = d u_a / d x_b.
nu	real(kind=R8P)	out		Eddy viscosity.

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sgs_sigma

Sigma eddy viscosity.

Attributes: pure

subroutine sgs_sigma(c, dl, delta, g, nu)

Arguments

Name	Type	Intent	Attributes	Description
c	real(kind=R8P)	in		Model constant C_sigma.
dl	real(kind=R8P)	in		Grid steps (unused).
delta	real(kind=R8P)	in		Filter width.
g	real(kind=R8P)	in		Velocity gradient, g(a,b) = d u_a / d x_b.
nu	real(kind=R8P)	out		Eddy viscosity.

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