adam_flume_ic_object

ADAM, FLUME initial conditions class definition.

Accepted [initial_conditions].(type):

• uniform: the state of region 1 everywhere, density and pressure perturbed by the signed relative amplitude s, rho (1 + s h1), p (1 + s h2), with h1, h2 in [-1, 1) hashed from the block Morton code and the cell indexes: the same on every rank decomposition and on every backend (no random generator state);
• isentropic-vortex: the free stream of region 1 plus an isentropic vortex of axis z centred at (x0, y0), of radius radius and velocity strength strength (Shu 1998, ICASE 97-65, section 5.1, written for any free stream): du = -strength/(2 pi) (y-y0)/radius exp((1-r^2)/2), dv = strength/(2 pi) (x-x0)/radius exp((1-r^2)/2), d(p/rho) = -(gamma-1)/gamma strength^2/(8 pi^2) exp(1-r^2), isentropic, r = |x-x0| / radius; an exact steady solution convected by the free stream;
• riemann-problem: piecewise-constant axis-aligned regions, a cell belongs to a region iff emin < center <= emax on every axis. A cell covered by no region is fatal: leaving it at zero density would divide by zero downstream;
• glm-pulse (MHD only, the GLM d'Alembert test, issue #41, MV-3): the state of region 1 plus a Gaussian pulse in the magnetic field along pulse_axis (x, y or z), B_axis += pulse_amplitude exp(-((s - pulse_center) / pulse_width)^2), s the cell coordinate along the axis; pressure and velocity unchanged (psi zero);
• divb-peak (MHD only, the Dedner et al. 2002 peak in B_x, issue #41, MV-10): the state of region 1 plus B_x += peak_amplitude (1 - (s / peak_radius)^2)^2 for s < peak_radius, s the distance in the x-y plane from (peak_x0, peak_y0) (Dedner: peak_amplitude = 1 / sqrt(4 pi), peak_radius = 1/8); a non-zero initial div(B);
• mhd-linear-wave (MHD only, issue #41, MV-5; Stone et al. 2008, section 8.2): the state q0 of region 1 (global frame) plus wave_amplitude R sin(2 pi (x cos a + y sin a) / wavelength), a = wave_angle (degrees, in the x-y plane), R the right eigenvector of the right-going wave (fast, alfven, slow or entropy) of the conservative system at q0 in the frame of the wave normal (the library Roe-Balsara core, mhd_eigenvectors), rotated back to x, y, z; after one period wavelength / |u_n + c| the exact solution is the initial state;
• mhd-cpaw (MHD only, issue #41, MV-6; Toth 2000, J. Comput. Phys. 161): the circularly polarised Alfven wave, an exact nonlinear solution of any amplitude. Density and pressure of region 1 (whose velocity and field must be zero), the field b_par n + wave_amplitude (sin(phi) t1 + h cos(phi) t2) and the velocity -sign(b_par) B_perp / sqrt(rho), phi = 2 pi (x cos a + y sin a) / wavelength, a = wave_angle (degrees), n = (cos a, sin a, 0), t1 = (-sin a, cos a, 0), t2 = z, h = +1 (polarisation = right) or -1 (left, the mirror image under z -> -z); |B_perp| is uniform, so the total pressure is too, and the wave travels along +n unchanged at |b_par| / sqrt(rho): after one period wavelength sqrt(rho) / |b_par| the exact solution is the initial state.

The primitive keys of a region follow the physical model: r, u, v, w, p (Euler), plus bx, by, bz (MHD; psi is zero). isentropic-vortex is Euler only (issue #41, section 3.7).

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

Dependencies

Contents

• flume_ic_object
• initialize
• load_from_file
• set_initial_conditions
• hash_cell
• linear_wave_eigenvector
• isentropic_vortex
• description

Variables

Name	Type	Attributes	Description
INI_SECTION_NAME	character(len=18)	parameter	INI section name.
IC_UNIFORM_STR	character(len=7)	parameter	Uniform state.
IC_ISENTROPIC_VORTEX_STR	character(len=17)	parameter	Isentropic vortex in a free stream.
IC_RIEMANN_PROBLEM_STR	character(len=15)	parameter	Piecewise-constant regions.
IC_GLM_PULSE_STR	character(len=9)	parameter	Gaussian pulse in B along an axis (MHD).
PULSE_KEY	character(len=15)	parameter	GLM pulse keys.
IC_DIVB_PEAK_STR	character(len=9)	parameter	Dedner peak in B_x (MHD).
PEAK_KEY	character(len=14)	parameter	div(B) peak keys.
IC_MHD_LINEAR_WAVE_STR	character(len=15)	parameter	MHD linear wave (MHD).
WAVE_KEY	character(len=14)	parameter	Linear wave and CPAW keys.
IC_MHD_CPAW_STR	character(len=8)	parameter	Circularly polarised Alfven wave (MHD).
VORTEX_KEY	character(len=8)	parameter	Vortex keys.
PI	real(kind=R8P)	parameter	Pi greek.
PRIM_KEY	character(len=2)	parameter	Region primitive state keys (MHD: all 8).
EXTENT_KEY	character(len=6)	parameter	Region extents keys.

Derived Types

flume_ic_object

FLUME initial conditions class definition.

Components

Name	Type	Attributes	Description
amr_iterations	integer(kind=I4P)		AMR iterations performed while imposing the initial conditions.
ic_type	character(len=:)	allocatable	Initial conditions type.
regions_number	integer(kind=I4P)		Regions number.
model	integer(kind=I4P)		Physical model id.
nprim	integer(kind=I4P)		Primitive keys number of a region: 5 (Euler) or 8 (MHD).
q_region	real(kind=R8P)	allocatable	Conservative state of each region [nv, regions_number].
emin	real(kind=R8P)	allocatable	Minimum corner of each region [3, regions_number].
emax	real(kind=R8P)	allocatable	Maximum corner of each region [3, regions_number].
gamma	real(kind=R8P)		Specific heats ratio.
prim_1	real(kind=R8P)		Primitive state of region 1, the free stream (first nprim used).
s	real(kind=R8P)		Uniform: relative amplitude of the seeded perturbation.
vortex	real(kind=R8P)		Isentropic vortex: x0, y0, radius, strength.
pulse_axis	integer(kind=I4P)		GLM pulse: axis, 1=x, 2=y, 3=z.
pulse	real(kind=R8P)		GLM pulse: center, width, amplitude.
peak	real(kind=R8P)		div(B) peak: x0, y0, radius, amplitude.
wave	character(len=:)	allocatable	Linear wave family: fast, alfven, slow, entropy.
wave_par	real(kind=R8P)		Linear wave, CPAW: angle (degrees), amplitude, wavelength.
wave_r	real(kind=R8P)		Linear wave: right eigenvector, global frame.
b_par	real(kind=R8P)		CPAW: field along the wave normal.
polarisation	real(kind=R8P)		CPAW: +1 right, -1 left.

Type-Bound Procedures

Name	Attributes	Description
description	pass(self)	Return pretty-printed object description.
initialize	pass(self)	Initialize initial conditions.
load_from_file	pass(self)	Load config from file.
set_initial_conditions	pass(self)	Set initial conditions on the blocks interior.

Subroutines

initialize

Initialize initial conditions.

subroutine initialize(self, file_parameters, physics)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_ic_object)	inout		Initial conditions.
file_parameters	type(file_ini)	in		Simulation parameters ini file handler.
physics	type(flume_physics_object)	in		Physics (for the regions state conversion).

Call graph

load_from_file

Load config from file; every key used by the selected type is required and an unknown type is fatal.

subroutine load_from_file(self, file_parameters, physics)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_ic_object)	inout		Initial conditions.
file_parameters	type(file_ini)	in		Simulation parameters ini file handler.
physics	type(flume_physics_object)	in		Physics (for the regions state conversion).

Call graph

set_initial_conditions

Set initial conditions on the blocks interior; ghost cells are filled by the following ghost update.

subroutine set_initial_conditions(self, field, q)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_ic_object)	in		Initial conditions.
field	type(field_object)	in		Field (realm component, threaded in).
q	real(kind=R8P)	inout		Conservative variables.

Call graph

hash_cell

Return two pseudo-random numbers in [-1, 1) that depend only on the block Morton code and the cell indexes.

Integer mixing with no integer overflow, so the same bits on every compiler; the cell key never depends on the rank that owns the block. The key is chained (mix the code, then fold in i, j, k one at a time and mix again), so keys whose bits overlap, such as small codes and small indexes, do not collide. Xorshift alone is linear over GF(2), which would make the numbers an affine function of the key bits (exactly equidistributed, spatially structured): each mix also multiplies by an odd constant modulo 2^52 (xorshift* idea, Vigna 2016), in 26-bit limbs to stay in range.

Attributes: pure

subroutine hash_cell(code, i, j, k, h)

Arguments

Name	Type	Intent	Attributes	Description
code	integer(kind=I8P)	in		Block Morton code.
i	integer(kind=I4P)	in		Cell indexes.
j	integer(kind=I4P)	in		Cell indexes.
k	integer(kind=I4P)	in		Cell indexes.
h	real(kind=R8P)	out		Pseudo-random numbers in [-1, 1).

Call graph

linear_wave_eigenvector

Return the right eigenvector of the right-going wave of the conservative MHD system at the primitive state prim (global frame), for the wave normal at angle degrees in the x-y plane: the state is rotated into the frame of the normal, R is the column of mhd_eigenvectors (x direction of that frame; waves ordered u_n - c_f, u_n - c_a, u_n - c_s, u_n, u_n + c_s, u_n + c_a, u_n + c_f, B_n), and its momentum and field are rotated back to x, y, z.

Attributes: pure

subroutine linear_wave_eigenvector(gamma, R, prim, wave, angle, r_global)

Arguments

Name	Type	Intent	Attributes	Description
gamma	real(kind=R8P)	in		Specific heats ratio.
R	real(kind=R8P)	in		Gas constant.
prim	real(kind=R8P)	in		Primitive state, global frame (r, u, v, w, p, bx, by, bz).
wave	character(len=*)	in		Wave family: fast, alfven, slow, entropy.
angle	real(kind=R8P)	in		Wave normal angle in the x-y plane (degrees).
r_global	real(kind=R8P)	out		Right eigenvector, global frame.

Call graph

isentropic_vortex

Return the conservative state of the isentropic vortex at (x, y) (formulas in the module documentation).

Attributes: pure

subroutine isentropic_vortex(gamma, prim, vortex, x, y, q)

Arguments

Name	Type	Intent	Attributes	Description
gamma	real(kind=R8P)	in		Specific heats ratio.
prim	real(kind=R8P)	in		Free stream primitive state (r, u, v, w, p).
vortex	real(kind=R8P)	in		Vortex x0, y0, radius, strength.
x	real(kind=R8P)	in		Point coordinates.
y	real(kind=R8P)	in		Point coordinates.
q	real(kind=R8P)	out		Conservative variables.

Call graph

Functions

description

Return a pretty-formatted object description.

Returns: character(len=:)

function description(self) result(desc)

Arguments

Name	Type	Intent	Attributes	Description
self	class(flume_ic_object)	in		Initial conditions.

Call graph