Shear-Layer Q8

This setup utilizes Q-polynomial representation and a spatial scheme order of 8. It simulates a velocity layer in a rectangular channel with slipwall boundaries. See the ateles.lua for the configuration:

-- Configuration file for Ateles --
require 'hyperfun'

-- global simulation options
simulation_name = 'shear_layer_modg' -- the name of the simualtion
sim_control = {
  time_control = {
    min = 0.0,
    max = 1.0e-05
  }
}

-- Mesh definitions --
mesh = 'mesh/'

-- Tracking
tracking = {
  label = 'probe_momentum_Q8',
  folder = '',
  variable = {'momentum'},
  shape = {kind = 'canoND', object= { origin ={0., 0., 0.} } },
  time_control = {
    min = 0,
    max = sim_control.time_control.max,
    interval = sim_control.time_control.max/2.0
  },
  output = { format = 'ascii', ndofs = 1 }
}

-- Equation definitions --
equation = {
    name   = 'euler',
    isen_coef = 1.4,
    r      = 296.0,
    material = {
      characteristic = 0,
      relax_velocity = {0, 0, 0},
      relax_temperature = 0
    }
}
-- (cv) heat capacity and (r) ideal gas constant
equation["cv"] = equation["r"] / (equation["isen_coef"] - 1.0)

-- Scheme definitions --
scheme = {
  -- the spatial discretization scheme
  spatial =  {
    name = 'modg',
    m =  7
  },
  -- the temporal discretization scheme
  temporal = {
    name = 'explicitRungeKutta',
    steps = 4,
    -- how to control the timestep
    control = {
      name = 'cfl',   -- the name of the timestep control mechanism
      cfl  = 0.6  -- CourantÐFriedrichsÐLewy number
    }
  }
}

projection = {
  kind = 'fpt',
  factor = 1.0
}

width = 0.07
xDist = 0.1
vel =  50.0
periods=2
function iniVelX(x,y,z)
  center = math.sin(periods*math.pi*x)*xDist
  return vel*tanh((y-center)/width)
end

initial_condition = {
  density = 1.225,
  pressure = 100000,
  velocityX = iniVelX,
  velocityY = 0.0,
  velocityZ = 0.0
}

boundary_condition = {
  {
    label = 'slipSouth',
    kind = 'slipwall'
  },
  {
    label = 'slipNorth',
    kind = 'slipwall'
  },
  {
    label = 'slipTop',
    kind = 'slipwall'
  },
  {
    label = 'slipBottom',
    kind = 'slipwall'
  }
}

Features used

  1. Projection: fpt

  2. Polynomial representation: Q

  3. Filtering: --

  4. Timestepping: explicitRungeKutta, 4 steps

  5. Boundary conditions: slipwall