adam_flume_inflow_df_object

ADAM, FLUME digital-filter turbulent inflow of a boundary layer (issue #119, T3.7).

One realm face of kind inflow-digital-filter feeds a turbulent boundary layer: the mean profile of a table plus fluctuations with prescribed Reynolds stresses and length scales, built by the digital filter of Klein, Sadiki & Janicka (2003) in the form of Touber & Sandham (2009) and Xie & Castro (2008):

1. Plane. A uniform grid of the face, df_spacing apart along the wall-normal and the spanwise axes (cell-centred nodes, the spacing adjusted to divide the domain), periodic along the span when that axis is periodic.
2. Filter. Uniform random numbers of zero mean and unit variance (MINSTD, one stream, so every rank builds the same plane and no communication is needed) are filtered along both plane axes with b_k = exp(-pi |k| / n) normalised to unit sum of squares, n = L / spacing the integral length in nodes, the stencil half-width 2 n: the filtered field has unit variance and the exponential correlation exp(-pi r / (2 L)).
3. Time. The streamwise correlation becomes a temporal one, psi = psi exp(-pi dt / (2 T)) + psi_new sqrt(1 - exp(-pi dt / T)), T = L_x / U_inf (Xie & Castro 2008): unit variance kept, correlation exp(-pi t / (2 T)).
4. Stresses. The three unit-variance signals become velocity fluctuations by the Cholesky factor of the Reynolds stress tensor of the table (Lund, Wu & Squires 1998), with R_13 = R_23 = 0: u' = a11 psi1, v' = a21 psi1 + a22 psi2, w' = a33 psi3.
5. Thermodynamics. The strong Reynolds analogy (Morkovin; Touber & Sandham 2009), T' / T = -(gamma - 1) M^2 u' / U with the local mean Mach number, written T' = -(gamma - 1) U u' rho / (gamma p) so it holds at U = 0; the pressure is the free-stream one, rho' / rho = -T' / T.

The table (df_profile, ASCII, # comments) has 7 columns: y / delta, U / U_inf, T / T_inf, R_uu, R_vv, R_ww, R_uv in units of U_inf^2, u streamwise, v wall-normal, w spanwise; the mean density is rho_inf T_inf / T (no pressure gradient across the layer). Beyond its last row the free stream, linearly interpolated within.

Face keys: type = inflow-digital-filter, r, u, p (the free stream: density, speed along the inward normal, pressure), df_profile, df_delta (the layer thickness), df_wall_axis (x, y or z, the wall on its minimum side), df_spacing, df_length_streamwise, df_length_normal, df_length_spanwise (integral lengths in units of df_delta), df_seed (default 1). Only [physics] physical_model = euler, one such face per realm.

Ghosts. Once per step (advance) the plane moves on by the step; build_rows then lists the ghost cells beyond the face (crown rows beyond that face only) and their states, interpolated bilinearly in the plane; the backends write them after the face pass of the boundary fill. Rows beyond the face and another realm face (edges, corners) are extrapolated. The plane state is saved with the restart (<restart_basename>.dff), so a restart continues bit for bit.

Source: src/app/flume/common/adam_flume_inflow_df_object.F90

Dependencies

Contents

• flume_inflow_df_object
• load
• setup
• advance
• build_rows
• save_state
• load_state
• load_profile
• profile_mean
• filter_coefficients
• filtered_field
• plane_states
• fluctuation
• plane_value
• next_uniform

Variables

Name	Type	Attributes	Description
PI	real(kind=R8P)	parameter	Pi.

Derived Types

flume_inflow_df_object

Digital-filter inflow.

Components

Name	Type	Attributes	Description
is_active	logical		A face of this kind exists.
face	integer(kind=I4P)		The face (1 to 6).
axis_n	integer(kind=I4P)		Streamwise axis (the face normal).
axis_w	integer(kind=I4P)		Wall-normal axis.
axis_s	integer(kind=I4P)		Spanwise axis.
sgn	real(kind=R8P)		Sign of the inward normal along axis_n.
r_inf	real(kind=R8P)		Free-stream density.
u_inf	real(kind=R8P)		Free-stream speed.
p_inf	real(kind=R8P)		Free-stream pressure.
gamma	real(kind=R8P)		Specific heats ratio.
delta	real(kind=R8P)		Layer thickness.
spacing	real(kind=R8P)		Requested plane spacing.
length	real(kind=R8P)		Integral lengths (streamwise, normal, spanwise) / delta.
seed	integer(kind=I8P)		Random stream state.
profile_file	character(len=999)		Profile table file.
prof	real(kind=R8P)	allocatable	Profile table [7, rows].
ny	integer(kind=I4P)		Plane nodes along the wall-normal and spanwise axes.
nz	integer(kind=I4P)		Plane nodes along the wall-normal and spanwise axes.
y0	real(kind=R8P)		Plane origin (the domain minimum along each axis).
z0	real(kind=R8P)		Plane origin (the domain minimum along each axis).
dy	real(kind=R8P)		Plane spacing along each axis.
dz	real(kind=R8P)		Plane spacing along each axis.
span_periodic	logical		The spanwise axis is periodic.
hy	integer(kind=I4P)		Filter half-widths in nodes.
hz	integer(kind=I4P)		Filter half-widths in nodes.
t_scale	real(kind=R8P)		Time scale T = L_x / U_inf.
by	real(kind=R8P)	allocatable	Filter coefficients [-h:h].
bz	real(kind=R8P)	allocatable	Filter coefficients [-h:h].
psi	real(kind=R8P)	allocatable	Unit-variance signals [3, ny, nz].
node_mean	real(kind=R8P)	allocatable	Per wall-normal node: U, rho, a11, a21, a22, a33 [6, ny].
q_plane	real(kind=R8P)	allocatable	Conservative state at the nodes [5, ny, nz].
nrows	integer(kind=I4P)		Ghost rows of the face on this rank.
rows	integer(kind=I4P)	allocatable	Their block and cell [4, nrows].
q_rows	real(kind=R8P)	allocatable	Their conservative states [5, nrows].

Type-Bound Procedures

Name	Attributes	Description
load	pass(self)	Load the face keys.
setup	pass(self)	Build the plane, the filter and the first signals.
advance	pass(self)	Move the signals on by one step.
build_rows	pass(self)	List the ghost rows of the face and their states.
fluctuation	pass(self)	Velocity and temperature fluctuations at a plane node.
save_state	pass(self)	Save the plane state.
load_state	pass(self)	Load the plane state.

Subroutines

load

Load the keys of the face face (section section).

subroutine load(self, file_parameters, section, face, model, gamma)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	inout		Inflow.
file_parameters	type(file_ini)	in		Parameters file.
section	character(len=*)	in		Face section.
face	integer(kind=I4P)	in		Face (1 to 6).
model	integer(kind=I4P)	in		Physical model.
gamma	real(kind=R8P)	in		Specific heats ratio.

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setup

Build the plane over the domain [emin, emax], the filter coefficients, the mean state of each wall-normal node, and the first signals (an independent filtered field, so the inflow is turbulent from the first step).

subroutine setup(self, emin, emax, periodic)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	inout		Inflow.
emin	real(kind=R8P)	in		Domain minimum.
emax	real(kind=R8P)	in		Domain maximum.
periodic	logical	in		Periodic axes.

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advance

Move the signals on by the step dt (Xie & Castro 2008) and refresh the node states.

subroutine advance(self, dt)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	inout		Inflow.
dt	real(kind=R8P)	in		Time step.

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build_rows

List the crown rows beyond the face only (block > 0) and their states, bilinear in the plane.

subroutine build_rows(self, crown_map, x_cell, y_cell, z_cell)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	inout		Inflow.
crown_map	integer(kind=I8P)	in		BC crown map [rows, 9, ngc].
x_cell	real(kind=R8P)	in		X cell centres [1-ngc:ni+ngc, nb] (passed 1-based).
y_cell	real(kind=R8P)	in		Y cell centres.
z_cell	real(kind=R8P)	in		Z cell centres.

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save_state

Save the plane state to <basename>.dff (rank 0; every rank holds the same state).

subroutine save_state(self, basename)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	in		Inflow.
basename	character(len=*)	in		Restart files basename.

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load_state

Load the plane state from <basename>.dff; without the file the signals restart from a fresh field (warned).

subroutine load_state(self, basename)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	inout		Inflow.
basename	character(len=*)	in		Restart files basename.

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load_profile

Load a profile table: 7 columns (y / delta, U / U_inf, T / T_inf, R_uu, R_vv, R_ww, R_uv / U_inf^2), # comments, rows in increasing y; fatal on a malformed table.

subroutine load_profile(filename, prof)

Arguments

Name	Type	Intent	Attributes	Description
filename	character(len=*)	in		File name.
prof	real(kind=R8P)	out	allocatable	Table [7, rows].

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profile_mean

Return the table's U / U_inf, T / T_inf and stresses (R_uu, R_vv, R_ww, R_uv) at eta = y / delta: linear within, the first row below it, the free stream (1, 1, 0) beyond the last row.

Attributes: pure

subroutine profile_mean(prof, eta, u, t, r)

Arguments

Name	Type	Intent	Attributes	Description
prof	real(kind=R8P)	in		Table [7, rows].
eta	real(kind=R8P)	in		y / delta.
u	real(kind=R8P)	out		Mean speed and temperature.
t	real(kind=R8P)	out		Mean speed and temperature.
r	real(kind=R8P)	out		Stresses.

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filter_coefficients

Coefficients b_k = exp(-pi |k| / n) normalised to unit sum of squares, half-width h = ceiling(2 n) (at least 1).

subroutine filter_coefficients(n, h, b)

Arguments

Name	Type	Intent	Attributes	Description
n	real(kind=R8P)	in		Integral length in nodes.
h	integer(kind=I4P)	out		Half-width.
b	real(kind=R8P)	out	allocatable	Coefficients [-h:h].

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filtered_field

A fresh filtered field of unit variance: random numbers on the plane padded by the half-widths (wrapped along a periodic span), filtered along the wall-normal then the spanwise axis.

subroutine filtered_field(self, psi)

Arguments

Name	Type	Intent	Attributes	Description
self	type(flume_inflow_df_object)	inout		Inflow.
psi	real(kind=R8P)	out		Field [3, ny, nz].

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plane_states

The conservative state at every node from the mean and the fluctuations.

subroutine plane_states(self)

Arguments

Name	Type	Intent	Attributes	Description
self	type(flume_inflow_df_object)	inout		Inflow.

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Functions

fluctuation

Velocity fluctuations (streamwise, wall-normal, spanwise) and temperature fluctuation over the mean temperature at the node (j, k).

Attributes: pure

Returns: real(kind=R8P)

function fluctuation(self, j, k) result(f)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_inflow_df_object)	in		Inflow.
j	integer(kind=I4P)	in		Node.
k	integer(kind=I4P)	in		Node.

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plane_value

The state at (y, z), bilinear between the nodes: clamped along the wall normal, wrapped (periodic span) or clamped along the span.

Attributes: pure

Returns: real(kind=R8P)

function plane_value(self, y, z) result(q)

Arguments

Name	Type	Intent	Attributes	Description
self	type(flume_inflow_df_object)	in		Inflow.
y	real(kind=R8P)	in		Coordinates along the wall-normal and spanwise axes.
z	real(kind=R8P)	in		Coordinates along the wall-normal and spanwise axes.

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next_uniform

MINSTD (Park & Miller 1993): the next value in (0, 1), portable, no overflow in 64 bits.

Returns: real(kind=R8P)

function next_uniform(r) result(v)

Arguments

Name	Type	Intent	Attributes	Description
r	integer(kind=I8P)	inout		State.

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