Data Structures
class	RungeKuttaWithDensityFloor
	Runge-Kutta Finite Differences which insert the density floor after each stage. More...

class	RusanovWithDensityFloor
	Finite Volumes which insert the density floor after each update. More...

Functions
	insert_density_floor (solver, time_step, tag, patch)
	Insert the density floor after each task of solver which carries tag.

	exact_density (x, t)

	create_solver (name, rk_order, density_floor)
	Create the Euler solver of the tutorial.

	plot_task_graph (rk_order, file_name, title)
	Construct the time stepping task graph including the density floor and draw it.

	build_and_run (rk_order, density_floor, directory, peano_root)

	density_along_x_axis (patch_file)
	Return time stamp plus grid cell centres and densities along y=0 of the last snapshot.

Variables
	Here = os.path.dirname(os.path.abspath(__file__))

	PeanoRoot = os.path.abspath(os.path.join(Here, "..", "..", ".."))

str	Flux

str	MaxEigenvalue

str	InitPointWisely

str	DensityFloor

float	DomainOffset = -0.1

float	DomainWidth = 0.2

float	VolumeSize = 0.0075

float	EndTime = 0.2

	parser

	default

	help

	args = parser.parse_args()

	work_directory

	fig

	axes

	figsize

	sharey

	x_fine = np.linspace(DomainOffset, DomainOffset + DomainWidth, 400)

	linewidth

	label

	directory

	patch_file

	t

	x

	rho

	markersize

	color

	linestyle

	loc

	bbox_to_anchor

	output = os.path.join(Here, "20_additional-solver-steps-profile.png")

	dpi

	bbox_inches

Function Documentation

◆ build_and_run()

20_additional-solver-steps.build_and_run	(	rk_order,
		density_floor,
		directory,
		peano_root
	)

Definition at line 249 of file 20_additional-solver-steps.py.

References create_solver().

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◆ create_solver()

20_additional-solver-steps.create_solver	(	name,
		rk_order,
		density_floor
	)

Create the Euler solver of the tutorial.

Parameters

rk_order int or None None selects the Finite Volumes, an integer the fourth-order Finite Differences with the Runge-Kutta scheme of this order.

Definition at line 179 of file 20_additional-solver-steps.py.

Referenced by build_and_run(), and plot_task_graph().

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◆ density_along_x_axis()

20_additional-solver-steps.density_along_x_axis ( patch_file )

Return time stamp plus grid cell centres and densities along y=0 of the last snapshot.

Definition at line 286 of file 20_additional-solver-steps.py.

References tarch.plotter.api.notebook.read_patches(), and tarch.plotter.api.notebook.read_snapshots().

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◆ exact_density()

20_additional-solver-steps.exact_density	(	x,
		t
	)

Definition at line 173 of file 20_additional-solver-steps.py.

◆ insert_density_floor()

20_additional-solver-steps.insert_density_floor	(	solver,
		time_step,
		tag,
		patch
	)

Insert the density floor after each task of solver which carries tag.

Mirrors the routine of the tutorial: The numerical scheme knows which patch its tagged tasks write and passes it in.

Definition at line 106 of file 20_additional-solver-steps.py.

Referenced by 20_additional-solver-steps.RusanovWithDensityFloor.construct_output(), and 20_additional-solver-steps.RungeKuttaWithDensityFloor.construct_output().

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◆ plot_task_graph()

20_additional-solver-steps.plot_task_graph	(	rk_order,
		file_name,
		title
	)

Construct the time stepping task graph including the density floor and draw it.

Definition at line 227 of file 20_additional-solver-steps.py.

References create_solver().

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Variable Documentation

◆ args

20_additional-solver-steps.args = parser.parse_args()

Definition at line 319 of file 20_additional-solver-steps.py.

◆ axes

20_additional-solver-steps.axes

Definition at line 338 of file 20_additional-solver-steps.py.

◆ bbox_inches

20_additional-solver-steps.bbox_inches

Definition at line 378 of file 20_additional-solver-steps.py.

◆ bbox_to_anchor

20_additional-solver-steps.bbox_to_anchor

Definition at line 376 of file 20_additional-solver-steps.py.

◆ color

20_additional-solver-steps.color

Definition at line 371 of file 20_additional-solver-steps.py.

◆ default

20_additional-solver-steps.default

Definition at line 311 of file 20_additional-solver-steps.py.

◆ DensityFloor

str 20_additional-solver-steps.DensityFloor

Initial value:

=  """
  constexpr double gamma      = 1.4;
  constexpr double minDensity = 0.9;
  if (Q[0] < minDensity) {
    const double u = Q[1] / Q[0];
    const double v = Q[2] / Q[0];
    const double p = (gamma - 1.0) * (Q[3] - 0.5 * Q[0] * (u * u + v * v));
    Q[0] = minDensity;
    Q[1] = minDensity * u;
    Q[2] = minDensity * v;
    Q[3] = p / (gamma - 1.0) + 0.5 * minDensity * (u * u + v * v);
  }
"""

Definition at line 90 of file 20_additional-solver-steps.py.

◆ directory

20_additional-solver-steps.directory

Initial value:

=  os.path.join(
                    work_directory,
                    "{}-{}".format(
                        "fv" if rk_order is None else "rk4",
                        "floor" if density_floor else "plain",
                    ),
                )

Definition at line 348 of file 20_additional-solver-steps.py.

◆ DomainOffset

float 20_additional-solver-steps.DomainOffset = -0.1

Definition at line 167 of file 20_additional-solver-steps.py.

◆ DomainWidth

float 20_additional-solver-steps.DomainWidth = 0.2

Definition at line 168 of file 20_additional-solver-steps.py.

◆ dpi

20_additional-solver-steps.dpi

Definition at line 378 of file 20_additional-solver-steps.py.

◆ EndTime

float 20_additional-solver-steps.EndTime = 0.2

Definition at line 170 of file 20_additional-solver-steps.py.

◆ fig

20_additional-solver-steps.fig

Definition at line 338 of file 20_additional-solver-steps.py.

◆ figsize

20_additional-solver-steps.figsize

Definition at line 338 of file 20_additional-solver-steps.py.

◆ Flux

str 20_additional-solver-steps.Flux

Initial value:

=  """
  const double irho  = 1.0 / Q[0];
  constexpr double gamma = 1.4;
  const double p = (gamma - 1.0) * (Q[3] - 0.5 * irho * (Q[1] * Q[1] + Q[2] * Q[2]));
  switch (normal) {
    case 0:
      F[0] = Q[1];
      F[1] = irho * Q[1] * Q[1] + p;
      F[2] = irho * Q[1] * Q[2];
      F[3] = irho * Q[1] * (Q[3] + p);
      break;
    case 1:
      F[0] = Q[2];
      F[1] = irho * Q[2] * Q[1];
      F[2] = irho * Q[2] * Q[2] + p;
      F[3] = irho * Q[2] * (Q[3] + p);
      break;
  }
"""

Definition at line 50 of file 20_additional-solver-steps.py.

◆ help

20_additional-solver-steps.help

Definition at line 312 of file 20_additional-solver-steps.py.

◆ Here

20_additional-solver-steps.Here = os.path.dirname(os.path.abspath(__file__))

Definition at line 33 of file 20_additional-solver-steps.py.

◆ InitPointWisely

str 20_additional-solver-steps.InitPointWisely

Initial value:

=  """
  constexpr double gamma = 1.4;
  constexpr double p     = 1.0;
  constexpr double u     = 1.0;
  const double     rho   = 1.0 + 0.2 * std::sin(2.0 * M_PI * (x[0] + 0.1) / 0.2);
  Q[0] = rho;
  Q[1] = rho * u;
  Q[2] = 0.0;
  Q[3] = p / (gamma - 1) + 0.5 * rho * u * u;
"""

Definition at line 79 of file 20_additional-solver-steps.py.

◆ label

20_additional-solver-steps.label

Definition at line 345 of file 20_additional-solver-steps.py.

◆ linestyle

20_additional-solver-steps.linestyle

Definition at line 371 of file 20_additional-solver-steps.py.

◆ linewidth

20_additional-solver-steps.linewidth

Definition at line 345 of file 20_additional-solver-steps.py.

◆ loc

20_additional-solver-steps.loc

Definition at line 376 of file 20_additional-solver-steps.py.

◆ markersize

20_additional-solver-steps.markersize

Definition at line 368 of file 20_additional-solver-steps.py.

◆ MaxEigenvalue

str 20_additional-solver-steps.MaxEigenvalue

Initial value:

=  """
  const double irho  = 1.0 / Q[0];
  constexpr double gamma = 1.4;
  const double p = (gamma - 1.0) * (Q[3] - 0.5 * irho * (Q[1] * Q[1] + Q[2] * Q[2]));
  const double c = std::sqrt(gamma * p * irho);
  const double u = Q[1 + normal] * irho;
  lambdaMax[0] = std::max(std::abs(u + c), std::abs(u - c));
"""

Definition at line 70 of file 20_additional-solver-steps.py.

◆ output

20_additional-solver-steps.output = os.path.join(Here, "20_additional-solver-steps-profile.png")

Definition at line 377 of file 20_additional-solver-steps.py.

◆ parser

20_additional-solver-steps.parser

Initial value:

=  argparse.ArgumentParser(
        description="Create the PNGs of the tutorial 20_additional-solver-steps.ipynb"
    )

Definition at line 306 of file 20_additional-solver-steps.py.

◆ patch_file

20_additional-solver-steps.patch_file

Initial value:

=  build_and_run(
                    rk_order, density_floor, directory, os.path.abspath(args.peano_root)
                )

Definition at line 355 of file 20_additional-solver-steps.py.

◆ PeanoRoot

20_additional-solver-steps.PeanoRoot = os.path.abspath(os.path.join(Here, "..", "..", ".."))

Definition at line 34 of file 20_additional-solver-steps.py.

◆ rho

20_additional-solver-steps.rho

Definition at line 358 of file 20_additional-solver-steps.py.

◆ sharey

20_additional-solver-steps.sharey

Definition at line 338 of file 20_additional-solver-steps.py.

◆ t

20_additional-solver-steps.t

Definition at line 358 of file 20_additional-solver-steps.py.

◆ VolumeSize

float 20_additional-solver-steps.VolumeSize = 0.0075

Definition at line 169 of file 20_additional-solver-steps.py.

◆ work_directory

20_additional-solver-steps.work_directory

Initial value:

=  os.path.abspath(
            args.work_directory or stack.enter_context(tempfile.TemporaryDirectory())
        )

Definition at line 335 of file 20_additional-solver-steps.py.

◆ x

20_additional-solver-steps.x

Definition at line 358 of file 20_additional-solver-steps.py.

◆ x_fine

20_additional-solver-steps.x_fine = np.linspace(DomainOffset, DomainOffset + DomainWidth, 400)

Definition at line 343 of file 20_additional-solver-steps.py.

Data Structures

Functions

Variables

Function Documentation

◆ build_and_run()

◆ create_solver()

◆ density_along_x_axis()

◆ exact_density()

◆ insert_density_floor()

◆ plot_task_graph()

Variable Documentation

◆ args

◆ axes

◆ bbox_inches

◆ bbox_to_anchor

◆ color

◆ default

◆ DensityFloor

◆ directory

◆ DomainOffset

◆ DomainWidth

◆ dpi

◆ EndTime

◆ fig

◆ figsize

◆ Flux

◆ help

◆ Here

◆ InitPointWisely

◆ label

◆ linestyle

◆ linewidth

◆ loc

◆ markersize

◆ MaxEigenvalue

◆ output

◆ parser

◆ patch_file

◆ PeanoRoot

◆ rho

◆ sharey

◆ t

◆ VolumeSize

◆ work_directory

◆ x

◆ x_fine