Neko
0.8.1
A portable framework for highorder spectral element flow simulations

The case file defines all the parameters of a simulation. The format of the file is JSON, making it easy to read and write case files using the majority of the popular programming languages. JSON is heirarchical and, and consists of parameter blocks enclosed in curly braces. These blocks are referred to as objects. The case file makes use objects to separate the configuration of different parts of the solver. We refer the reader to the examples shipped with the code to get a good idea of how a case file looks. The table below provides a complete reference for all possible configuration choices.
The current highlevel structure of the case file is shown below.
The version
keywords is reserved to track changes in the format of the file. The the subsections below we list all the configuration options for each of the highlevel objects. Some parameters will have default values, and are therefore optional.
A common scheme for controlling the output frequency is applied for various outputs. It is described already now in order to clarify the meaning of several parameters found in the tables below.
The frequency is controlled by two paramters, ending with _control
and _value
, respectively. The latter name is perhaps not ideal, but it is somewhat difficult to come up with a good one, suggestions are welcome.
The _value
parameter is a number, that defines the output frequency, but the interpretation of that number depends on the choice of _control
. The three following options are possible.
simulationtime
, then _value
is the time interval between the outputs.tsteps
, then _value
is the number of time steps between the outputs.nsamples
, then _value
is the total number of outputs that will be performed in the course of the simulation.never
, then _value
is ignored and output is never performed.This object is mostly used as a highlevel container for all the other objects, but also defines several parameters that pertain to the simulation as a whole.
Name  Description  Admissible values  Default value 

mesh_file  The name of the mesh file.  Strings ending with .nmsh   
output_boundary  Whether to write a bdry0.f0000 file with boundary labels. Can be used to check boundary conditions.  true or false  false 
output_directory  Folder for redirecting solver output. Note that the folder has to exist!  Path to an existing directory  . 
output_precision  Whether to output snapshots in single or double precision  single or double  single 
load_balancing  Whether to apply load balancing.  true or false  false 
output_partitions  Whether to write a partitions.vtk file with domain partitioning.  true or false  false 
output_checkpoints  Whether to output checkpoints, i.e. restart files.  true or false  false 
checkpoint_control  Defines the interpretation of checkpoint_value to define the frequency of writing checkpoint files.  nsamples , simulationtime , tsteps , never   
checkpoint_value  The frequency of sampling in terms of checkpoint_control .  Positive real or integer   
restart_file  checkpoint to use for a restart from previous data  Strings ending with .chkp   
timestep  Timestep size  Positive reals   
variable_timestep  Whether to use variable dt  true or false  false 
max_timestep  Maximum timestep size when variable time step is activated  Positive reals   
target_cfl  The desired CFL number  Positive real  0.4 
cfl_max_update_frequency  The minimum interval between two timestepupdating steps in terms of time steps  Integer  0 
cfl_running_avg_coeff  The running average coefficient a where cfl_avg_new = a * cfl_new + (1a) * cfl_avg_old  Positive real between 0 and 1  0.5 
max_dt_increase_factor  The maximum scaling factor to increase time step  Positive real greater than 1  1.2 
min_dt_decrease_factor  The minimum scaling factor to decrease time step  Positive real less than 1  0.5 
end_time  Final time at which the simulation is stopped.  Positive reals   
job_timelimit  The maximum wall clock duration of the simulation.  String formatted as HH:MM:SS  No limit 
output_boundary
field When the output_boundary
setting is set to true
, and additional .fld
file will be stored in the beginning of the simulation, where the recognized boundaries will be marked with an integer number. This is a good way to debug the simulation setup. The value of the number depends on the type of the boundary as follows:
w
label.v
label.o
label.sym
label.on
label.Note that the boundary conditions can be both prescribed via the labels in the case file or built into the mesh via conversion from a .re2
file. Both types will be picked up and marked in the field produced by output_boundary
.
Used to define the properties of the numerical discretization.
Name  Description  Admissible values  Default value 

polynomial_order  The oder of the polynomial basis.  Integers, typically 5 to 9   
time_order  The order of the time integration scheme. Refer to the time_scheme_controller type documention for details.  1,2, 3   
dealias  Whether to apply dealiasing to advection terms.  true or false  false 
dealiased_polynomial order  The polynomial order in the higherorder space used in the dealising.  Integer  3/2(polynomial_order + 1)  1 
The configuration of the fluid solver and the flow problem. Contains multiple subobjects for various parts of the setup.
As per the governing equations, Neko requires the value of the density and dynamic viscosity to define the flow problem. These can be provided as rho
and mu
in the case file.
Alternatively, one may opt to provide the Reynolds number, Re
, which corresponds to a nondimensional formulation of the NavierStokes equations. This formulation can effectively be obtained by setting \( \rho = 1 \) and \( \mu = 1/Re \). This is exactly what Neko does under the hood, when Re
is provided in the case file.
Note that if both Re
and any of the dimensional material properties are provided, the simulation will issue an error.
As an alternative to providing material properties in the case file, it is possible to do that in a special routine in the user file. This is demonstrated in the rayleighbenardcylinder
example. Ultimately, both rho
and mu
have to be set in the subroutine, but it can be based on arbitrary computations and arbitrary parameters read from the case file. Additionally, this allows to change the material properties in time.
The optional boundary_types
keyword can be used to specify boundary conditions. The reason for it being optional, is that some conditions can be specified directly inside the mesh file. In particular, this happens when Nek5000 .re2
files are converted to .nmsh
. Periodic boundary conditions are always defined inside the mesh file.
The value of the keyword is an array of strings, with the following possible values:
w
, a noslip wall.v
, a velocity Dirichlet boundary.sym
, a symmetry boundary.o
, outlet boundary.on
, Dirichlet for the boundaryparallel velocity and homogeneous Neumann for the wallnormal. The wallparallel velocity is defined by the initial condition.d_vel_u
, d_vel_v
, d_vel_w
(or a combination of them, separated by a "/"
), a Dirichlet boundary for more complex velocity profiles. This boundary condition uses a more advanced user interface.d_pres
, a boundary for specified nonuniform pressure profiles, similar in essence to d_vel_u
,d_vel_v
and d_vel_w
. Can be combined with other complex Dirichlet coonditions by specifying e.g.: "d_vel_u/d_vel_v/d_pres"
.o+dong
, outlet boundary using the Dong condition.on+dong
, an on
boundary using the Dong condition, ensuring that the wallnormal velocity is directed outwards.In some cases, only some boundary types have to be provided. For example, when one has periodic boundaries, like in the channel flow example. In this case, to put the specification of the boundary at the right index, preceding boundary types can be marked with an empty string. For example, if boundaries with index 1 and 2 are periodic, and the third one is a wall, we can set.
The object inflow_condition
is used to specify velocity values at a Dirichlet boundary. This does not necessarily have to be an inflow boundary, so the name is not so good, and will most likely be changed along with type changes in the code. Since not all cases have Dirichlet boundaries (note, the special case of a noslip boundary is treated separately in the configuration), this object is not obligatory. The means of prescribing the values are controlled via the type
keyword:
user
, the values are set inside the compiled user file.uniform
, the value is a constant vector, looked up under the value
keyword.blasius
, a Blasius profile is prescribed. Its properties are looked up in the case.fluid.blasius
object, see below.The object initial_condition
is used to provide initial conditions. It is mandatory. Note that this currently pertains to both the fluid, but also scalars. The means of prescribing the values are controlled via the type
keyword:
user
, the values are set inside the compiled user file. The only way to initialize scalars.uniform
, the value is a constant vector, looked up under the value
keyword.blasius
, a Blasius profile is prescribed. Its properties are looked up in the case.fluid.blasius
object, see below.The blasius
object is used to specify the Blasius profile that can be used for the initial and inflow condition. The boundary cannot be tilted with respect to the coordinate axes. It requires the following parameters:
delta
, the thickness of the boundary layer.freestream_velocity
, the velocity value in the free stream.approximation
, the numerical approximation to the Blasius profile.linear
, linear approximation.quadratic
, quadratic approximation.cubic
, cubic approximation.quartic
, quartic approximation.sin
, sine function approximation.The source_terms
object should be used to specify the source terms in the momentum equation. The object is not mandatory, by default no forcing term is present. Each source term, is itself a JSON object, so source_terms
is just an array of them. Note that with respect to the governing equations, the source terms define \( f^u \), meaning that the values are then multiplied by the density.
For each source, the type
keyword defines the kind of forcing that will be introduced. Furthermore, the start_time
and end_time
keywords can be used to set a time frame for when the source term is active. Note, however, that these keywords have no effect on the userdefined source terms, but their execution can, of course, be directly controlled in the user code. By default, all source terms are active during the entire simulation.
The following types are currently implemented.
constant
, constant forcing. Strength defined by the values
array with 3 reals corresponding to the 3 components of the forcing.boussinesq
, a source term introducing boyancy based on the Boussinesq approximation, \( \rho \beta (T  T_{ref} \cdot g) \). Here, \( rho \) is density, \( \beta \) the thermal expansion coefficient, \( g \) the gravity vector, and $T_{ref}$ a reference value of the scalar, typically temperature.
Reads the following entries:
scalar_field
: The name of the scalar that drives the source term, defaults to "s".reference_value
: The reference value of the scalar.g
: The gravity vector.beta
: The thermal expansion coefficient, defaults to the inverse of ref_value
.user_pointwise
, the values are set inside the compiled user file, using the pointwise user file subroutine. Only works on CPUs!user_vector
, the values are set inside the compiled user file, using the nonpointwise user file subroutine. Should be used when running on the GPU.brinkman
, Brinkman permeability forcing inside a predefined region.The Brinkman source term introduces regions of resistance in the fluid domain. The volume force \( f_i \) applied in the selected regions are proportional to the fluid velocity component \( u_i \).
\begin{eqnarray*} f_i(x) &=&  B(x) u_i(x), \\ B(x) &=& \kappa_0 + (\kappa_1  \kappa_0) \xi(x) \frac{q + 1}{q + \xi(x)}, \end{eqnarray*}
where, \( x \) is the current location in the domain, \( \xi: x \mapsto [0,1] \) represent an indicator function for the resistance where \( \xi(x) = 0 \) is a free flow. \( \kappa_i \) describes the limits for the force application at \( \xi(x)=0 \) and \( \xi(x)=1 \). A penalty parameter \( q \) help us to reduce numerical problems.
The indicator function will be defined based on the object type. The following types are currently implemented.
boundary_mesh
, the indicator function for a boundary mesh is computed in two steps. First, the signed distance function is computed for the boundary mesh. Then, the indicator function is computed using the distance transform function specified in the case file.point_zone
, the indicator function is defined as 1 inside the point zone and 0 outside.Each object are added to a common indicator field by means of a pointwise max operator. This means that the indicator field will be the union of all the regions defined by the objects.
To assist correct placement and scaling of objects from external sources, the meshes can be transformed using the mesh_transform
object. The object can be used to apply a transformation to the boundary mesh. The following types are currently implemented.
none
, no transformation is applied.bounding_box
, the boundary mesh is transformed to fit inside a box defined by box_min
and box_max
. The box is defined by two vectors of 3 reals each. The keep_aspect_ratio
keyword can be used to keep the aspect ratio of the boundary mesh.After the indicator field is computed, it is filtered using a filter type specified in the case file. The filter is used to smooth the indicator field before computing the Brinkman force. The following types are currently implemented.
none
, no filtering is applied.The filtering can be defined for each object separately. Additionally, the filter can be specified for the entire source term, in which case it will be applied to the final indicator field, after all sources have been added.
Additional keywords are available to modify the Brinkman force term.
Name  Description  Admissible values  Default value 

brinkman.limits  Brinkman factor at freeflow ( \( \kappa_0 \)) and solid domain ( \( \kappa_1 \)).  Vector of 2 reals.   
brinkman.penalty  Penalty parameter \( q \) when estimating Brinkman factor.  Real  \( 1.0 \) 
objects  Array of JSON objects, defining the objects to be immersed.  Each object must specify a type   
distance_transform.type  How to map from distance field to indicator field.  step , smooth_step   
distance_transform.value  Values used to define the distance transform, such as cutoff distance for the step function.  Real   
filter.type  Type of filtering applied to the indicator field either globally or for the current object.  none  none 
mesh_transform.type  Apply a transformation to the boundary mesh.  bounding_box , none  none 
mesh_transform.box_min  Lower left front corner of the box to fit inside.  Vector of 3 reals   
mesh_transform.box_max  Upper right back corner of the box to fit inside.  Vector of 3 reals   
mesh_transform.keep_aspect_ratio  Keep the aspect ratio of the boundary mesh.  true or false  true 
Example of a Brinkman source term where a boundary mesh and a point zone are combined to define the resistance in the fluid domain. The indicator field for the boundary mesh is computed using a step function with a cutoff distance of \( 0.1 \). The indicator field for the point zone is not filtered.
The mandatory velocity_solver
and pressure_solver
objects are used to configure the solvers for the momentum and pressurePoisson equation. The following keywords are used, with the corresponding options.
type
, solver type.cg
, a conjugate gradient solver.pipecg
, a pipelined conjugate gradient solver.bicgstab
, a biconjugate gradient stabilized solver.cacg
, a communicationavoiding conjugate gradient solver.gmres
, a GMRES solver. Typically used for pressure.fusedcg
, a conjugate gradient solver optimised for accelerators using kernel fusion.preconditioner
, preconditioner type.jacobi
, a Jacobi preconditioner. Typically used for velocity.hsmg
, a hybridSchwarz multigrid preconditioner. Typically used for pressure.ident
, an identity matrix (no preconditioner).absolute_tolerance
, tolerance criterion for convergence.max_iterations
, maximum number of iterations before giving up.projection_space_size
, size of the vector space used for accelerating the solution procedure. If 0, then the projection space is not used. More important for the pressure equation.projection_hold_steps
, steps for which the simulation does not use projection after starting or time step changes. E.g. if 5, then the projection space will start to update at the 6th time step and the space will be utilized at the 7th time step.The optional flow_rate_force
object can be used to force a particular flow rate through the domain. Useful for channel and pipe flows. The configuration uses the following parameters:
direction
, the direction of the flow, defined as 0, 1, or 2, corresponding to x, y or z, respectively.value
, the desired flow rate.use_averaged_flow
, whether value
specifies the domainaveraged (bulk) velocity or the volume flow rate.All the parameters are summarized in the table below. This includes all the subobjects discussed above, as well as keyword parameters that can be described concisely directly in the table.
Name  Description  Admissible values  Default value 

scheme  The fluid solve type.  pnpn   
Re  The Reynolds number.  Positive real   
rho  The density of the fluid.  Positive real   
mu  The dynamic viscosity of the fluid.  Positive real   
output_control  Defines the interpretation of output_value to define the frequency of writing checkpoint files.  nsamples , simulationtime , tsteps , never   
output_value  The frequency of sampling in terms of output_control .  Positive real or integer   
inflow_condition.type  Velocity inflow condition type.  user , uniform , blasius   
inflow_condition.value  Value of the inflow velocity.  Vector of 3 reals   
initial_condition.type  Initial condition type.  user , uniform , blasius   
initial_condition.value  Value of the velocity initial condition.  Vector of 3 reals   
blasius.delta  Boundary layer thickness in the Blasius profile.  Positive real   
blasius.freestream_velocity  Freestream velocity in the Blasius profile.  Vector of 3 reals   
blasius.approximation  Numerical approximation of the Blasius profile.  linear , quadratic , cubic , quartic , sin   
source_terms  Array of JSON objects, defining additional source terms.  See list of source terms above   
boundary_types  Boundary types/conditions labels.  Array of strings   
velocity_solver.type  Linear solver for the momentum equation.  cg , pipecg , bicgstab , cacg , gmres   
velocity_solver.preconditioner  Linear solver preconditioner for the momentum equation.  ident , hsmg , jacobi   
velocity_solver.absolute_tolerance  Linear solver convergence criterion for the momentum equation.  Positive real   
velocity_solver.maxiter  Linear solver max iteration count for the momentum equation.  Positive real  800 
velocity_solver.projection_space_size  Projection space size for the momentum equation.  Positive integer  20 
velocity_solver.projection_hold_steps  Holding steps of the projection for the momentum equation.  Positive integer  5 
pressure_solver.type  Linear solver for the momentum equation.  cg , pipecg , bicgstab , cacg , gmres   
pressure_solver.preconditioner  Linear solver preconditioner for the momentum equation.  ident , hsmg , jacobi   
pressure_solver.absolute_tolerance  Linear solver convergence criterion for the momentum equation.  Positive real   
pressure_solver.maxiter  Linear solver max iteration count for the momentum equation.  Positive real  800 
pressure_solver.projection_space_size  Projection space size for the momentum equation.  Positive integer  20 
pressure_solver.projection_hold_steps  Holding steps of the projection for the momentum equation.  Positive integer  5 
flow_rate_force.direction  Direction of the forced flow.  0, 1, 2   
flow_rate_force.value  Bulk velocity or volumetric flow rate.  Positive real   
flow_rate_force.use_averaged_flow  Whether bulk velocity or volumetric flow rate is given by the value parameter.  true or false   
freeze  Whether to fix the velocity field at initial conditions.  true or false  false 
The scalar object allows to add a scalar transport equation to the solution. The solution variable is called s
, but saved as temperature
in the fld files. Some properties of the object are inherited from fluid
: the properties of the linear solver, the value of the density, and the output control.
The scalar equation requires defining additional material properties: the specific heat capacity and thermal conductivity. These are provided as cp
and lambda
. Similarly to the fluid, one can provide the Peclet number, Pe
, as an alternative. In this case, cp
is set to 1 and lambda
to the inverse of Pe
.
The boundary conditions for the scalar are specified through the boundary_types
keyword. It is possible to directly specify a uniform value for a Dirichlet boundary. The syntax is, e.g. d=1
, to set the value to 1, see the RyleighBenard example case.
The configuration of source terms is the same as for the fluid. A demonstration of using source terms for the scalar can be found in the scalar_mms
example.
Name  Description  Admissible values  Default value 

enabled  Whether to enable the scalar computation.  true or false  true 
Pe  The Peclet number.  Positive real   
cp  Specific heat cpacity.  Positive real   
lambda  Thermal conductivity.  Positive real   
boundary_types  Boundary types/conditions labels.  Array of strings   
initial_condition.type  Initial condition type.  user , uniform   
initial_condition.value  Value of the velocity initial condition.  Real   
source_terms  Array of JSON objects, defining additional source terms.  See list of source terms above   
This object adds the collection of statistics for the fluid fields. For additional details on the workflow, see the corresponding page in the user manual.
Name  Description  Admissible values  Default value 

enabled  Whether to enable the statistics computation.  true or false  true 
start_time  Time at which to start gathering statistics.  Positive real  0 
sampling_interval  Interval, in timesteps, for sampling the flow fields for statistics.  Positive integer  10 
Simulation components enable the user to perform various additional operations, which are not strictly necessary to run the solver. An example could be computing and output of additional fields, e.g. vorticity.
A more detailed description as well as a full list of available components and their setup is provided in a separate page of the manual.
Point zones enable the user to select GLL points in the computational domain according to some geometric criterion. Two predefined geometric shapes are selectable from the case file, boxes and spheres.
A point zone object defined in the case file can be retrieved from the point zone registry, neko_point_zone_registry
, and can be used to perform any zonespecific operations (e.g. localized source term, probing...). Userspecific point zones can also be added manually to the point zone registry from the user file.
A more detailed description as well as a full list of available components and their setup is provided in a separate page of the manual.