This is the lodi validation case from Poinsot and Lele (Boundary Conditions for Direct Simulations of Compressible Viscous Flows) but setup to test the restart capability of ablate.

Parameters

parameters	formula	value
l		.5
L		1
pInf		101325.0
rhoInit		1.0
gamma		1.4
Rgas		287.0
c	sqrt(gamma*p/rho)	~ 376.6178434435
uo	1.1*c	414.2796277878
Re	uo * l/nu = rho * uo * l /mu	10,000
mu	(rho * uo * l)/Re	0.02071398139

Vortex Params

parameters	value
C/(cl)	-.0005
C	-0.09415446086
Rc = 0.15*l	0.075

Fields

• \[u_x = uo - C/(rho*Rc^2) * exp((-x^2 - y^2)/(2*Rc^2))*y\]
• \[u_y = + C/(rho*Rc^2) * exp((-x^2 - y^2)/(2*Rc^2))*x\]
• \[p = pinf + (rho*C^2)/Rc^2 * exp(-(x^2 - y^2)/(2*Rc^2))\]
• \[T = p/(Rgas*rho) = 1/(Rgas*rho) * (pinf + (rho*C^2)/Rc^2 * exp(-(x^2 - y^2)/(2*Rc^2)))\]
• \[timeEnd = 2*l/c = 0.002655211423\]

compressibleFlow/compressibleFlowVortexLodiRestart.yaml

---
test: !IntegrationRestartTest
  # specify the basic test parameters for restart test
  testParameters:
    # a unique test name for this integration tests
    name: compressibleFlowVortexLodiRestart
    asserts:
      - "inputs/compressibleFlow/compressibleFlowVortexLodiRestart.txt"
  # upon restart, override some of the input parameters
  restartOverrides:
    timestepper::arguments::ts_max_steps: "20"

# metadata for the simulation
environment:
  title: _compressibleFlowVortex
  tagDirectory: false
arguments: {}
# set up the time stepper responsible for marching in time
timestepper:
  name: theMainTimeStepper
  # the Hdf5MultiFileSerializer writes each timestep state to a different file.  Using a serializer allows for the simulation to be viewed and restarted
  io: !ablate::io::Hdf5MultiFileSerializer
    interval: 0

  # time stepper specific input arguments.
  arguments:
    ts_type: rk
    ts_adapt_type: physics # overwrite and set the time step based upon the CFL constraint
    ts_max_steps: 10
    ts_max_time: 0.002655211423
    ts_adapt_safety: 1.0

    # the BoxMeshBoundaryCells domain adds an extra layer of boundary cells to the outside of the domain and
    # tags these cells with special labels
  domain: !ablate::domain::BoxMeshBoundaryCells
    name: simpleBoxField
    faces: [ 25, 25]
    lower: [ 0.0, -.5 ]
    upper: [ 1.0, .5 ]
    # pass in these options to petsc when setting up the domain.  Using an option list here prevents command line arguments from being seen.
    options:
      dm_refine: 0 # must be zero when using the BoxMeshBoundaryCells
    preModifiers:
      # if using mpi, this modifier distributes cells
      - !ablate::domain::modifiers::DistributeWithGhostCells

    # add any modifications after the ghost boundaries have been set up
    postModifiers:
      # to simplify setup, the boundaryCellsRight, boundaryCellsTop, boundaryCellsBottom are all labeled as openBoundaryLabel
      - !ablate::domain::modifiers::MergeLabels
        mergedRegion:
          name: openBoundaryLabel
        regions:
          - name: boundaryCellsRight
          - name: boundaryCellsTop
          - name: boundaryCellsBottom
      # if using a FVM ghost boundary cells must be added
      - !ablate::domain::modifiers::GhostBoundaryCells
    fields:
      # all fields must be defined before solvers.  The ablate::finiteVolume::CompressibleFlowFields is a helper
      # class that creates the required fields for the compressible flow solver (rho, rhoE, rhoU, ...)
      - !ablate::finiteVolume::CompressibleFlowFields
        eos: !ablate::eos::PerfectGas &eos
          parameters:
            gamma: 1.4
            Rgas : 287.0
        # define the field only over the domain cells, this prevents cells from being defined in unused corners
        region:
          name: domain
  # set the initial conditions of the flow field
  initialization:
    # all fields must be defined before solvers.  The ablate::finiteVolume::CompressibleFlowFields is a helper
    # class that creates the required fields for the compressible flow solver (rho, rhoE, rhoU, ...)
    - !ablate::finiteVolume::fieldFunctions::Euler
      state:
        eos: *eos
        pressure:
          !ablate::mathFunctions::Formula # the formula mathFunction allows specifying constants to use in the formula
          formula: pinf + (rho*C^2)/Rc^2 * exp(-((x-l)^2 + (y)^2)/(2*Rc^2))
          constants:
            # define the constants used by the formulas and shared with the temperature and velocity
            &constants
            pinf: 101325.0
            rho: 1.0
            gamma: 1.4
            Rgas: 287.0
            Rc: 0.075
            C: -0.09415446086
            uo: 414.2796277878
            l: .5
        temperature:
          !ablate::mathFunctions::Formula
          formula: 1/(Rgas*rho) * (pinf + (rho*C^2)/Rc^2 * exp(-((x-l)^2 +(y)^2)/(2*Rc^2)))
          constants: *constants
        velocity:
          !ablate::mathFunctions::Formula
          formula: uo - C/(rho*Rc^2) * exp((-(x-l)^2 - (y)^2)/(2*Rc^2))*y, C/(rho*Rc^2) * exp((-(x-l)^2 - (y)^2)/(2*Rc^2))*(x-l)
          constants: *constants
solvers:
  # The compressible flow solver will solve the compressible flow equations over the interiorCells
  - !ablate::finiteVolume::CompressibleFlowSolver
    id: vortexFlowField
    region:
      name: interiorCells

    # a flux calculator must be specified to so solver for advection
    fluxCalculator: !ablate::finiteVolume::fluxCalculator::AusmpUp
      mInf: .3

    # cfl is used to compute the physics time step
    parameters:
      cfl: 0.5

    # the default transport object assumes constant values for k, mu, diff
    transport:
      mu:  0.02071398139
    monitors:
      # output the max, min average value of the euler field at every time step
      - !ablate::monitors::MaxMinAverage
        field: euler

    # share the existing eos with the compressible flow solver
    eos: *eos

  # use a boundary solver to update the cells in the boundaryCellsLeft region to represent an inlet
  - !ablate::boundarySolver::BoundarySolver
    id: inlet
    region:
      name: boundaryCellsLeft
    fieldBoundary:
      name: boundaryFaces
    processes:
      - !ablate::boundarySolver::lodi::Inlet
        eos: *eos
  # use a boundary solver to update the cells in the openBoundaryLabel region to represent an open boundary
  - !ablate::boundarySolver::BoundarySolver
    id: openBoundary
    region:
      name: openBoundaryLabel
    fieldBoundary:
      name: boundaryFaces
    processes:
      - !ablate::boundarySolver::lodi::OpenBoundary
        eos: *eos
        reflectFactor: 0.0
        referencePressure: 101325.0
        maxAcousticsLength: 1