This section describes running the testcase using the Euler equations. Here we would take a small cubic geometry and define a gauss-pulse in density, i.e we set the initial density such that it has the peak in the center of the cube and it decreases towards the sides making a gaussian-pulse. Then we would give some velocity in one spatial direction (here, we choose x- direction), and watch this pulse in density move through the cube.
We assume that you already have read the General Procedure for Running the Testcases and the General Input File Information.
In this tutorial, we will show
and examine the input file for the Euler testcase.
Because this input file is specifically designed for the Euler testcase,
it does not make use of all the available options.
A complete input file with all available settings
can be found in the ateles folder ateles/ateles.lua.
For clarity we first define some variables, which we will use later.
We will simulate a gaussian pulse in density using modal
DG scheme,
hence here we would just name it as gPulseDens_euler_modg.
In this example we are going to simulate seconds
(max = cubeLength/velocityX/4).
Every 10th iteration information
about the current timestep is printed to the screen.
-- the length of the cube
cubeLength = 2.0
-- the refinement level of the octree
level = 1
-- transport velocity of the pulse in x direction.
velocityX = 100
-- global simulation options
simulation_name = 'gPulseDens_euler_modg' -- the name of the simualtion
sim_control = {
time_control = {
interval = { iter = 10 },
min = 0,
max = cubeLength / velocityX / 4, -- final simulation time
}
}
For the geometry we choose a predefined cube with periodic bounderaies and no obstacles.
-- mesh definitions
mesh = {
predefined = 'cube',
origin = {
(-1.0) * cubeLength / 2.0,
(-1.0) * cubeLength / 2.0,
(-1.0) * cubeLength / 2.0
},
length = cubeLength,
refinementLevel = level
}
Here for our case we will specify an initial condition
for the gauss-pulse in density (i.e set the initial density
such that it has a peak in the middle of the domain,
and decreases quickly towards the sides)
and make it travel in the x-direction.
This could also be a check for your boundary conditions
or just to visualize your numerical error
that smears out this gauss-pulse in time.
So, we set the velocityY and velcoityZ to zero
and give some value to the velcoityX and pressure.
For density we have a set of predefined variables
providing necessary information for the gauss pulse.
-- initial conditions
initial_condition = {
density = {
predefined = 'gausspulse',
center = { 0.0, 0.0, 0.0 }, -- gauss pulse center
halfwidth = 0.20, -- half width of gauss pulse from center
amplitude = 2.0, -- height or magnitude of gauss pulse
background = 1.225 -- reference value. In case of density, it is reference density.
},
pressure = 100000,
velocityX = velocityX,
velocityY = 0.0,
velocityZ = 0.0,
}
For the variable spatial we use the predefined name modg
which represents the modal Discontinuous Galerkin Scheme.
Similarly, for the time stepping scheme we have the variable temporal.
We use the predefined explicitRungeKutta
and are able to perform multi-step
Runge-Kutta
by setting the steps.
To control the timesteps we use the
CFL number
which can be specified in the control variable.
-- scheme definitions
scheme = {
-- the spatial discretization scheme
spatial = {
name = 'modg', -- we use the modal discontinuous Galerkin scheme
m = 6, -- the maximal polynomial degree for each spatial direction
dealiasFactor = 1.0, -- factor to remove aliases: 1.0 means no additional dealiasing
blocksize = 32, -- the minimal blocksize for the FPT
fftMultiThread = true -- use multithreaded version of FFTW
},
-- the temporal discretization scheme
temporal = {
name = 'explicitRungeKutta', -- 'explicitEuler'
steps = 4,
-- how to control the timestep
control = {
name = 'cfl', -- the name of the timestep control mechanism
cfl = 0.8 -- Courant_Friedrichs_Lewy number
}
}
}
The equations that we solve are the Euler equations
and it can be given through the input name in the equation table.
-- equation definitions
equation = {
name = 'euler', -- we solve euler equations
therm_cond = 2.555e-02, -- thermal conductivity (default = 6.953195-310)
isen_coef = 1.4, -- isentropic coefficient
r = 296.0, -- ideal gas constant
material = {
characteristic = 'global_characteristic',
relax_velocity = 'global_relax_velocity',
relax_temperature = 'global_relax_temperature'
}
}
-- (cv) heat capacity
equation["cv"] = equation["r"] / (equation["isen_coef"] - 1.0)
Here we define the global material for Euler 3D. It consists of three different components:
Thus we need five scalars for this equation system. As this is the global fallback material, we define each material to be a neutral term, which in this case is 0.
-- material variables
variable = {
{
name = "global_characteristic",
ncomponents = 1,
vartype = "st_fun",
st_fun = { const = 0.0 }
},
{
name = "global_relax_velocity",
ncomponents = 3,
vartype = "st_fun",
st_fun = {
const = { 0.0, 0.0, 0.0 }
}
},
{
name = "global_relax_temperature",
ncomponents = 1,
vartype = "st_fun",
st_fun = { const = 0.0 }
}
}
We want dumping restarts every 10th itertion till the end of the simulation.
Because we are not restarting from a file the variable read is commented out.
-- configuration for the restart file
restart = {
---- file to restart from
--read = './restart/gPulseDens_euler_modg_lastHeader.lua',
-- folder to write restart data to
write = './restart/',
-- temporal definition of restart write
time_control = {
interval = { iter = 10 },
min = 0,
max = sim_control.time_control.max,
}
}