# Input files specification

Rhoxyz, version 2020.4

## File format

JavaScript Object Notation (JSON) open–standard file format, that uses human readable text in form of attribute–value pairs and array data types, is used as an input for the solver. Graphical setting up of simulations may be implemented, but JSON format is intuitive enough to make as rapid changes as graphical interface could.

The table describing data types used for parameters is given below:

Name | Description | Example |
---|---|---|

integer | Simple non-decimal value. | `3` |

number | Any decimal or non-decimal value. | `1.234` |

string | Text stored in quotes. | `"this is a string"` |

list of numbers | List of any number of values. | `[3.2, 4, 566.3, 0.0]` |

list of strings | List of quoted texts. | `["qwe", "asd", "xcv"]` |

vector | List of 2 or 3 numbers. | `[2.0, 44.53, 0.0]` |

timeline of scalars | List of time–scalar pairs. | `[ [0, 2.0], [1.2, -1.0] ]` |

timeline of vectors | List of time–vector pairs. | `[ [0, [2.0, 2.3]], [1.2, [-1.0, 2.1]] ]` |

boolean | Value saying something is enabled or disabled. | `true` or `false` |

object | Something that contains multiple data information. | `"object_name": { data goes here }` |

**Note:** When a default value is available for some parameter, user does not need to specify the parameter (unless they want to override it).

**Note:** The document is an object, i.e. it must start with curly brackets ’{’ and ’}’. Also, the last element in a list or object must not have comma after its definition.

## General parameters

Global parameters of the simulation are listed as follows:

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“dimensions” | integer | must be specified | 2 (for 2D simulations) or 3 (for 3D simulations). |

“precision” | string | `single` |
Machine representation of numbers.`single` (for 32-bit precision)`double` (for 64-bit precision). |

“description” | string | Optional textual description of the simulation. | |

“name” | string | file name | The name of the simulation is by default same as the file name. User can override it. |

“device” | string | `best` |
On which device to execute the simulation.`cpu` (to use CPU cores)`gpu` (to execute it on a NVIDIA GPU)`best` to execute on the best device in the system. |

**Note:** The modern GPU can execute simulations > 20 times faster than the modern CPU. This holds for typical GPUs optimized for 32-bit precision operations (GTX, RTX, etc.). If double precision is needed, GPUs like Quadro, Tesla, etc. will perform better.

**Note:** 32-bit precision is usually enough if fast approximated/engineering results are needed. For extra large simulations, the implementation of accurate computation independent of precision is a work-in-process.

**Example:** JSON file with some general parameters.

```
{
"description": "Sway sloshing experiment blah blah",
"dimensions": 3,
"precision": "single",
... other parameters go here ...
}
```

## Relaxation

Relaxation is tightly connected to the scheme and pressure parameters. It says how strong factors dictate the simulation convergence within the time step.

“relaxation”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“space” | number | `1.0` |
How strong to force divergence cleaning based on the points arrangement information. |

“time” | number | `1.0` |
How strong to force divergence cleaning in the current time step. |

“walls” | number | `1.0` |
How strong to adapt to no-slip boundary condition in a single time step, i.e. adapt fluid acceleration near wall to the wall movement. |

“diagonal” | number | `0.0` |
How much to relax or smooth–out the system of linear equations (and the solution), by artificially scaling matrix diagonal to achieve better diagonal dominance. This should be a small number, e.g. from `1e-6` up to `1e-4` . |

}

**Note:** The scheme takes minimum value of space– and time–based relaxation. Space–based relaxation is preferable, since it’s less prone to induce oscillations.

**Note:** Diagonal scaling may help solvability of the system of equations, but yields a bit lower or smoothed out results than they should be.

**Example:**

```
"relaxation": {
"space": 0.9,
"walls": 1.0
}
```

## Pressure

Smooth and accurate pressure field is obtained by solving a Poisson equation. The equation is transformed to a system of linear equations, which is solved by using an iterative solver.

“pressure”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“solver” | string | `bicgstab` |
Type of the iterative solver:`bicgstab` non-preconditioned BiCGStab`pbicgstab` diagonally-preconditioned BiCGStab`qmrcgstab` non-preconditioned QMRCGStab`pqmrcgstab` diagonally-preconditioned QMRCGStab`cg` non-preconditioned CG`pcg` diagonally-preconditioned CG`jacobi` Jacobi solver |

“max_iterations” | integer | `150` |
Maximum number of iterations for trying to reach error lower than specified. |

“max_error” | number | `1e-3` |
Tolerance or maximum allowed relative error trying to be reached. |

“gradient_limiter” | number | `0.0` |
How much to limit overshooting within strong pressure gradient-areas. It is usually a value between 0.0 and 2.0, where higher values may be used for violent pressure fields to achieve large time-steps. |

}

**Example:**

```
"pressure": {
"solver": "bicgstab",
"max_iterations": 300,
"max_error": 1e-4,
"gradient_limiter": 1.0
}
```

## Velocity

Velocity is calculated from the momentum equation. For convection-dominated flows, it may be calculated directly, by explicitly approximating the diffusion. For diffusion-dominated flows, the velocity field should be solved implicitly using an iterative solver.

“velocity”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“solver” | string | `explicit` |
Type of the solver:`explicit` for solving velocity explicitly`jacobi` implicit Jacobi solver |

“max_iterations” | integer | `100` |
If using the implicit solver, maximum number of iterations trying to reach error lower than specified. |

“max_error” | number | `1e-4` |
If using the implicit solver, maximum allowed relative error trying to be reached. |

}

**Example:**

```
"velocity": {
"solver": "jacobi",
"max_iterations": 300,
"max_error": 1e-4
}
```

## Resolution

This category specifies the spacing between nearest neighbors, and the interaction radius. Each point can be connected to only first ring of its neighbours (fast, less diffusive), but better stability may be achieved by enlarging the radius to reach second ring of its neighbours (slower, more diffusive).

“resolution”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“spacing” | number | must be specified | The initial spacing between neighbouring points. This is analogous to the base cell size in mesh–based methods. |

“truncation” | number | `1.8` |
Interaction radius in terms of “number of spacings” to reach neighbouring points. It should be a value between 1.3 and 2.9. |

}

**Note:** Currently the point cloud resolution is constant in space and time, adaptive refinement is work in progress.

**Example:**

```
"resolution": {
"spacing": 0.02,
"truncation": 2.1
}
```

## Reordering

Each time step points perform Lagrangian advection, i.e. they move along solved streamlines. It can lead to distortion of the point distribution, and therefore mass conservation errors (imagine a rotating disc where points move in the tangential direction and increase the volume of the disc). On the Lagrangian movement, points are trying to keep equidistant neighbours to optimally conserve mass at all time.

“reordering”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“iterations” | integer | `4` |
Number of iterations to converge to constant neighbour spacing. The number may be from `1` to `20` . |

“radius” | number | `1.5` |
Interaction radius in terms of “number of spacings” for optimizing the point spacing. The value may be from `1.35` up to `1.80` . |

“compression” | number | `1.0` |
Allowed relative compression compared to the initial neighbourhood. Smaller compression may lead to better, but more aggressive re-organization of points. |

}

## External acceleration

Here we use term gravity as constant acceleration imposed to whole fluid in the domain, at all time. On the other hand, user may impose variable domain movement, which yields variable domain acceleration in time. This may be achieved by setting movement keyframes, or by analytically defining harmonic oscillator.

**Note:** During the simulation, gravity constant, keyframe motion, and oscillation motion are superposed.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“gravity” | vector | `[0, 0, 0]` |
Constant external acceleration vector. |

“impose_position” | timeline of vectors | [] | Domain position keyframes. Converted to external acceleration by second derivative. |

“impose_velocity” | timeline of vectors | [] | Domain velocity keyframes. Converted to external acceleration by first derivative. |

“impose_acceleration” | timeline of vectors | [] | Directly impose acceleration |

“impose_oscillation” | object | {} | See explanation below. |

The harmonic oscillator object is created as follows:

“impose_oscillation”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“frequency” | number | Oscillation frequency, rad/s. Not needed if the period is specified. | |

“period” | number | Oscillation period, s. Not needed if the frequency is specified. | |

“direction” | vector | Vector specifying the direction of translationj. It’s magnitude defines the amplitude of movement. | |

“axis” | vector | Vector specifying the axis of rotation. It’s magnitude defines the amplitude of movement. | |

“damping” | number | Damping ratio. |

}

**Note:** Setting domain rotation through keyframes is work-in-progress.

## Domain

The domain is an axis-aligned minimum bounding box (or AABB), defined by the starting and ending coordinates of its diagonal. It specifies the space where fluid flow is allowed. Currently, the domain size is static, dynamic adaptation of the domain size will be implemented.

“domain”: {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“min” | vector | must be specified | Minimum coordinates of the domain AABB. |

“max” | vector | must be specified | Maximum coordinates of the domain AABB. |

}

**Note:** Points leaving the domain boundaries are removed from the simulation.

**Note:** Performance will suffer if user specifies too large domain compared to the space of the fluid body.

**Example:**

```
"domain": {
"min": [0, 0, 1],
"max": [5, 1, 3.2]
}
```

## Patches

The simulation input file does not incorporate any volumetric mesh, but only bounding surfaces (patches) of the domain and objects in the scene. These surfaces can be defined using primitives (list of connected line–segments, quadrilaterals) or imported from the commonly used mesh file formats. Patches can be moveable, i.e. their motions can be imposed similarly as domain motions.

**Note:** The input is an object `patches`

containing any number of named boundary surfaces.

“patches:” {

“name_of_patch:” {

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“type” | string | `no_slip` |
Type or boundary condition of the surface. Currently available values are:`solid` or `no_slip` that imposes no-slip boundary condition,`free_slip` that imposes free-slip or no-penetration boundary condition,`free_surface` that marks virtual free surface of the fluid body. |

“geometry” | string | must be specified | How to define the geometry of the patch:`polyline` to define 2D connected line segments,`triangle` to define a single 3D triangle,`quad` to define a single 3D quad,`mesh_relative_path.stl` to load triangulated 3D surface from STL file format,`mesh_relative_path.obj` to load triangulated 3D surface from OBJ file format,`mesh_relative_path.off` to load triangulated 3D surface from OFF file format,`mesh_relative_path.ply` to load triangulated 3D surface from PLY file format. |

“points” | list of vectors | [] | Manually input list of vertices for the polyline, triangle or quad. |

“cog” | vector | `[0, 0, 0]` |
Initial center-of-gravity location around which the object rotates, and calculates the torque. |

“position” | vector | `[0, 0, 0]` |
Initial translation. |

“rotation” | vector | `[0, 0, 0]` |
Initial rotation. |

“probes” | list of vectors | [] | List of positions where to measure the pressure. The specified probes move with the patch. |

“impose_position” | timeline of vectors | [] | Impose motion of the patch as translation keyframes. |

“impose_velocity” | timeline of vectors | [] | Impose motion of the patch as translation velocity keyframes. |

“impose_acceleration” | timeline of vectors | [] | Impose motion of the patch as translation acceleration keyframes. |

“impose_rotation” | timeline of vectors | [] | Impose motion of the patch as translation keyframes. |

“impose_angular_velocity” | timeline of vectors | [] | Impose motion of the patch as translation velocity keyframes. |

“impose_angular_acceleration” | timeline of vectors | [] | Impose motion of the patch as translation acceleration keyframes. |

“impose_oscillation” | object | {} | See explanation above in section Domain. |

},

“another_patch: { … }”

}

**Note:** Generally, it’s not wise to use STL meshes (anywhere!) as they do not incorporate triangle connectivity information. If you still wish to use this format, solver will automatically connect triangles.

**Example:**

```
"patches": {
"tank": {
"type": "solid",
"geometry": "polyline",
"points": [
[-0.3, 0.3], [-0.3, 0.0], [ 0.3, 0.0], [ 0.3, 0.3], [-0.3, 0.3]
],
"oscillation": {
"period": 1.5,
"direction": [0.05, 0]
},
"probes": [
[-0.3, 0.1],
[0.3, 0.1]
]
},
"water": {
"type": "free_surface",
"geometry": "polyline",
"points": [ [-1, 0.12], [1, 0.12] ]
}
}
```

## Fluid

Currently a single fluid phase is supported, but soon multi-phase and variable-phase calculation will be implemented. The specified single fluid moves in the domain specified above. When the boundary surfaces are defined, user may fill the domain space with fluid.

**Note:** The fluid set-up follows the same as idea as bucket fill or flood fill tools in painting programs. Fluid is filled from some source point until it reaches wall and free-surface boundaries, defined above.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“density” | number | `1000` |
Constant density of the fluid phase, . |

“viscosity” | number | `1e-6` |
Constant kinematic viscosity of the fluid phase, . |

“surface_tension” | number | `0.0` |
Surface tension coefficient between the fluid phase and (unmodeled) other light phase, . |

“flood_point” | vector | [] | The point where to start flooding from. |

“flood_points” | list of vectors | [] | If multiple separated spaces need to be filled with same fluid, then specify a list of points where to flood from. |

“type” | string | `newtonian` |
How the fluid (viscosity) is modelled.`newtonian` for Newtonian fluids,`bingham` for Bingham-type viscoplastics,`casson` for Casson-type viscoplastics,`power_law` for Power Law model,`cross_power_law` for Cross-Power Law model,`bird_carreau` for Bird-Carreau model,`mohr_coulomb` for geophysical Mohr-Coulomb model. |

```
"fluid": {
"density": 998.6,
"viscosity": 1.14e-6,
"flood_point": [0.0, 0.05]
}
```

## Non-Newtonian models

If the fluid type is not Newtonian, but some non-Newtonian type, then the below listed parameters should be set. Currently available non-Newtonian models are: `bingham`

, `casson`

, `power_law`

, `cross_power_law`

, `bird_carreau`

, `mohr_coulomb`

.

**Note:** The viscosities of non-Newtonian models are input as *dynamic*, instead of *kinematic*. This may change in the future, or there may be a switch.

### Bingham

Models a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. Once the critical shear stress (yield stress) is exceeded, the material flows in such a way that the shear rate is proportional to the amount by which the applied shear stress exceeds the yield stress.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“viscosity” | number | must be specified | Dynamic viscosity at infinite shear rate. |

“yield_stress” | number | `0` |
The critical shear stress that sets a threshold for flowing. |

“regularization” | number | `500` |
Avoids the singularity of the model. Higher number allows higher viscosity near the singularity. |

### Casson Model

Similar to the Bingham model, for simulating shear-thickening behaviour of non-Newtonian fluids, for modelling viscoplastic fluids.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“viscosity_inf” | number | must be specified | Dynamic viscosity at infinite shear rate. |

“yield_stress” | number | `0` |
The critical shear stress that sets a threshold for flowing. |

“regularization” | number | `500` |
Avoids the singularity of the model. Higher number allows higher viscosity near the singularity. |

### Power Law

Power-law or the Ostwald–de Waele relationship, is a type of approximate generalised Newtonian fluid (time independent Non-Newtonian fluid). It yields good flow description across the range of shear rates to which the coefficients were fitted.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

“viscosity_min” | number | must be specified | Lower bound value of dynamic viscosity. |

“viscosity_max” | number | must be specified | Upper bound value of dynamic viscosity. |

“flow_index” | number | `0.5` |
, dimensionless flow behaviour index. Pseudoplastic: , Newtonian: , Dilatant: . |

"consistency_index" | number | `0` |
, flow consistency index or or power-law coefficient. |

### Cross-Power Law model

A type of generalised Newtonian fluid whose viscosity depends upon shear rate according to the following equation. The zero-shear viscosity is approached at very low shear rates, while the infinite shear viscosity is approached at very high shear rates.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

"viscosity_0" | number | must be specified | Value of dynamic viscosity at zero shear rate. |

"viscosity_inf" | number | must be specified | Value of dynamic viscosity at infinite shear rate. |

"flow_index" | number | `0.5` |
, dimensionless flow behaviour index. Pseudoplastic: , Newtonian: , Dilatant: . |

"time_change" | number | `0` |
Relaxation time in seconds, at which the linear behaviour changes to power law. 0 for Newtonian behaviour. |

### Bird-Carreau Model

A model that is valid over the complete range of shear rates. For cases where there are significant variations from the Power law model, i.e. at very high and very low shear rates it becomes essential to incorporate the values of viscosity at zero shear and at infinite shear into the formulation.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

"viscosity_0" | number | must be specified | Value of dynamic viscosity at zero shear rate. |

"viscosity_inf" | number | must be specified | Value of dynamic viscosity at infinite shear rate. |

"flow_index" | number | `0.5` |
, dimensionless flow behaviour or power index. |

"time_change" | number | `0` |
Time in seconds at which the linear behaviour changes to power law. 0 for Newtonian behaviour. |

"time_relaxation" | number | `0` |
Relaxation time constant. |

### Mohr-Coulomb Model

A model describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Generally the theory applies to materials for which the compression strength far exceeds the tensile strength.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

"viscosity" | number | must be specified | Dynamic viscosity of the fluid phase. |

"friction_angle" | number | `30` |
, internal friction angle in degrees. |

"cohesion" | number | `0` |
, cohesion in pressure units, Pascals. |

"regularization" | number | `500` |
Avoids the singularity of the model. Higher number allows higher viscosity near the singularity. |

## Output

Besides real-time viewing of the results, the results may be written to hard drive to post-process them in another software. Currently the results may be written to VTK legacy ASCII file–format, which can be read by ParaView.

Parameter name | Data type | Default value | What to input |
---|---|---|---|

"time_step" | number | Time interval to repeatedly output results. Zero value ignores outputting. | |

"times" | list of numbers | If not via the time–step, user may require simulation to write its results at specific times. | |

"boundary_points" | boolean | `true` |
Whether to export points generated for boundary conditions or not. |

"fields" | list of strings | `["pressure", "velocity"]` |
List of solved information to export. Available values are:`pressure` `pressure_gradient` `velocity` `velocity_divergence` `vorticity` |

**Note:** The folder for outputting is created where the input file is located.

**Note:** Along with output fields, the solver writes: *log, forces & torques, pressure probes.*

**Example:**

```
"output": {
"time_step": 0.2,
"times": [0.1666, 1.53],
"fields": ["velocity", "vorticity"]
}
```