Weakly Compressible Finite Volume Navier Stokes
The weakly compressible implementation of the Navier Stokes equations in finite volume is largely based of the incompressible version, except that constant densities were replaced by functor material properties. The incompressible kernels were adapted to use the functor material properties, so most kernels can be adapted directly. The only kernels that different between the two formulations are the time derivative kernels, as they include the density time derivative.
In addition, the NavierStokesFV action syntax can also be used to set up weakly-compressible simulations.
Lid Driven Cavity Heated Flow
We show below an example input file for a cavity with a moving lid, with different heat sources on both sides of the cavity.
mu = 1
rho = 'rho'
k = 1
cp = 1
l = 10
velocity_interp_method = 'rc'
advected_interp_method = 'average'
cold_temp=300
hot_temp=310
[GlobalParams]
two_term_boundary_expansion = true
rhie_chow_user_object = 'rc'
[]
[UserObjects]
[rc]
type = INSFVRhieChowInterpolator
u = u
v = v
pressure = pressure
[]
[]
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
xmin = 0
xmax = ${l}
ymin = 0
ymax = ${l}
nx = 16
ny = 16
[]
[]
[Variables]
[u]
type = INSFVVelocityVariable
initial_condition = 1e-15
[]
[v]
type = INSFVVelocityVariable
initial_condition = 1e-15
[]
[pressure]
type = INSFVPressureVariable
initial_condition = 1e5
[]
[T]
type = INSFVEnergyVariable
scaling = 1e-4
initial_condition = ${cold_temp}
[]
[]
[AuxVariables]
[U]
order = CONSTANT
family = MONOMIAL
fv = true
[]
[vel_x]
order = FIRST
family = MONOMIAL
[]
[vel_y]
order = FIRST
family = MONOMIAL
[]
[viz_T]
order = FIRST
family = MONOMIAL
[]
[]
[AuxKernels]
[mag]
type = VectorMagnitudeAux
variable = U
x = u
y = v
execute_on = 'initial timestep_end'
[]
[vel_x]
type = ParsedAux
variable = vel_x
expression = 'u'
execute_on = 'initial timestep_end'
coupled_variables = 'u'
[]
[vel_y]
type = ParsedAux
variable = vel_y
expression = 'v'
execute_on = 'initial timestep_end'
coupled_variables = 'v'
[]
[viz_T]
type = ParsedAux
variable = viz_T
expression = 'T'
execute_on = 'initial timestep_end'
coupled_variables = 'T'
[]
[]
[FVKernels]
[mass_time]
type = WCNSFVMassTimeDerivative
variable = pressure
drho_dt = drho_dt
[]
[mass]
type = INSFVMassAdvection
variable = pressure
advected_interp_method = ${advected_interp_method}
velocity_interp_method = ${velocity_interp_method}
rho = ${rho}
[]
[u_time]
type = WCNSFVMomentumTimeDerivative
variable = u
drho_dt = drho_dt
rho = rho
momentum_component = 'x'
[]
[u_advection]
type = INSFVMomentumAdvection
variable = u
velocity_interp_method = ${velocity_interp_method}
advected_interp_method = ${advected_interp_method}
rho = ${rho}
momentum_component = 'x'
[]
[u_viscosity]
type = INSFVMomentumDiffusion
variable = u
mu = ${mu}
momentum_component = 'x'
[]
[u_pressure]
type = INSFVMomentumPressure
variable = u
momentum_component = 'x'
pressure = pressure
[]
[u_gravity]
type = INSFVMomentumGravity
variable = u
gravity = '0 -1 0'
rho = ${rho}
momentum_component = 'x'
[]
[v_time]
type = WCNSFVMomentumTimeDerivative
variable = v
drho_dt = drho_dt
rho = rho
momentum_component = 'y'
[]
[v_advection]
type = INSFVMomentumAdvection
variable = v
velocity_interp_method = ${velocity_interp_method}
advected_interp_method = ${advected_interp_method}
rho = ${rho}
momentum_component = 'y'
[]
[v_viscosity]
type = INSFVMomentumDiffusion
variable = v
mu = ${mu}
momentum_component = 'y'
[]
[v_pressure]
type = INSFVMomentumPressure
variable = v
momentum_component = 'y'
pressure = pressure
[]
[v_gravity]
type = INSFVMomentumGravity
variable = v
gravity = '0 -1 0'
rho = ${rho}
momentum_component = 'y'
[]
[temp_conduction]
type = FVDiffusion
coeff = 'k'
variable = T
[]
[temp_advection]
type = INSFVEnergyAdvection
variable = T
velocity_interp_method = ${velocity_interp_method}
advected_interp_method = ${advected_interp_method}
[]
[]
[FVBCs]
[no_slip_x]
type = INSFVNoSlipWallBC
variable = u
boundary = 'left right top bottom'
function = 0
[]
[no_slip_y]
type = INSFVNoSlipWallBC
variable = v
boundary = 'left right top bottom'
function = 0
[]
[T_hot]
type = FVDirichletBC
variable = T
boundary = left
value = ${hot_temp}
[]
[T_cold]
type = FVDirichletBC
variable = T
boundary = right
value = ${cold_temp}
[]
[]
[FluidProperties]
[fp]
type = IdealGasFluidProperties
[]
[]
[Materials]
[const_functor]
type = ADGenericFunctorMaterial
prop_names = 'cp k'
prop_values = '${cp} ${k}'
[]
[rho]
type = RhoFromPTFunctorMaterial
fp = fp
temperature = T
pressure = pressure
[]
[ins_fv]
type = INSFVEnthalpyMaterial
temperature = 'T'
rho = ${rho}
[]
[]
[Functions]
[lid_function]
type = ParsedFunction
expression = '4*x*(1-x)'
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type -pc_factor_shift_type'
petsc_options_value = 'lu NONZERO'
steady_state_detection = true
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e-5
optimal_iterations = 6
[]
nl_abs_tol = 1e-9
normalize_solution_diff_norm_by_dt = false
nl_max_its = 10
[]
[Outputs]
[out]
type = Exodus
[]
[]
(moose/modules/navier_stokes/test/tests/finite_volume/ins/boussinesq/transient-wcnsfv.i)Heated Channel Flow
We show below an example input file for a heated channel. The fluid progressively heats up through the channel, with a volumetric heat source.
rho = 'rho'
l = 10
velocity_interp_method = 'rc'
advected_interp_method = 'average'
# Artificial fluid properties
# For a real case, use a GeneralFluidFunctorProperties and a viscosity rampdown
# or initialize very well!
k = 1
cp = 1000
mu = 1e2
# Operating conditions
inlet_temp = 300
outlet_pressure = 1e5
inlet_v = 0.001
[Mesh]
[gen]
type = GeneratedMeshGenerator
dim = 2
xmin = 0
xmax = ${l}
ymin = 0
ymax = 1
nx = 20
ny = 10
[]
[]
[GlobalParams]
rhie_chow_user_object = 'rc'
[]
[UserObjects]
[rc]
type = INSFVRhieChowInterpolator
u = vel_x
v = vel_y
pressure = pressure
[]
[]
[Variables]
[vel_x]
type = INSFVVelocityVariable
initial_condition = ${inlet_v}
[]
[vel_y]
type = INSFVVelocityVariable
initial_condition = 1e-15
[]
[pressure]
type = INSFVPressureVariable
initial_condition = ${outlet_pressure}
[]
[T_fluid]
type = INSFVEnergyVariable
initial_condition = ${inlet_temp}
[]
[]
[AuxVariables]
[mixing_length]
type = MooseVariableFVReal
[]
[power_density]
type = MooseVariableFVReal
initial_condition = 1e4
[]
[]
[FVKernels]
inactive = 'u_turb v_turb temp_turb'
[mass_time]
type = WCNSFVMassTimeDerivative
variable = pressure
drho_dt = drho_dt
[]
[mass]
type = INSFVMassAdvection
variable = pressure
advected_interp_method = ${advected_interp_method}
velocity_interp_method = ${velocity_interp_method}
rho = ${rho}
[]
[u_time]
type = WCNSFVMomentumTimeDerivative
variable = vel_x
drho_dt = drho_dt
rho = rho
momentum_component = 'x'
[]
[u_advection]
type = INSFVMomentumAdvection
variable = vel_x
velocity_interp_method = ${velocity_interp_method}
advected_interp_method = ${advected_interp_method}
rho = ${rho}
momentum_component = 'x'
[]
[u_viscosity]
type = INSFVMomentumDiffusion
variable = vel_x
mu = ${mu}
momentum_component = 'x'
[]
[u_pressure]
type = INSFVMomentumPressure
variable = vel_x
momentum_component = 'x'
pressure = pressure
[]
[u_turb]
type = INSFVMixingLengthReynoldsStress
variable = vel_x
rho = ${rho}
mixing_length = 'mixing_length'
momentum_component = 'x'
u = vel_x
v = vel_y
[]
[v_time]
type = WCNSFVMomentumTimeDerivative
variable = vel_y
drho_dt = drho_dt
rho = rho
momentum_component = 'y'
[]
[v_advection]
type = INSFVMomentumAdvection
variable = vel_y
velocity_interp_method = ${velocity_interp_method}
advected_interp_method = ${advected_interp_method}
rho = ${rho}
momentum_component = 'y'
[]
[v_viscosity]
type = INSFVMomentumDiffusion
variable = vel_y
momentum_component = 'y'
mu = ${mu}
[]
[v_pressure]
type = INSFVMomentumPressure
variable = vel_y
momentum_component = 'y'
pressure = pressure
[]
[v_turb]
type = INSFVMixingLengthReynoldsStress
variable = vel_y
rho = ${rho}
mixing_length = 'mixing_length'
momentum_component = 'y'
u = vel_x
v = vel_y
[]
[temp_time]
type = WCNSFVEnergyTimeDerivative
variable = T_fluid
cp = cp
rho = rho
drho_dt = drho_dt
[]
[temp_conduction]
type = FVDiffusion
coeff = 'k'
variable = T_fluid
[]
[temp_advection]
type = INSFVEnergyAdvection
variable = T_fluid
velocity_interp_method = ${velocity_interp_method}
advected_interp_method = ${advected_interp_method}
[]
[heat_source]
type = FVCoupledForce
variable = T_fluid
v = power_density
[]
[temp_turb]
type = WCNSFVMixingLengthEnergyDiffusion
variable = T_fluid
rho = rho
cp = cp
mixing_length = 'mixing_length'
schmidt_number = 1
u = vel_x
v = vel_y
[]
[]
[FVBCs]
[no_slip_x]
type = INSFVNoSlipWallBC
variable = vel_x
boundary = 'top bottom'
function = 0
[]
[no_slip_y]
type = INSFVNoSlipWallBC
variable = vel_y
boundary = 'top bottom'
function = 0
[]
# Inlet
[inlet_u]
type = INSFVInletVelocityBC
variable = vel_x
boundary = 'left'
function = ${inlet_v}
[]
[inlet_v]
type = INSFVInletVelocityBC
variable = vel_y
boundary = 'left'
function = 0
[]
[inlet_T]
type = FVDirichletBC
variable = T_fluid
boundary = 'left'
value = ${inlet_temp}
[]
[outlet_p]
type = INSFVOutletPressureBC
variable = pressure
boundary = 'right'
function = ${outlet_pressure}
[]
[]
[FluidProperties]
[fp]
type = FlibeFluidProperties
[]
[]
[Materials]
[const_functor]
type = ADGenericFunctorMaterial
prop_names = 'cp k'
prop_values = '${cp} ${k}'
[]
[rho]
type = RhoFromPTFunctorMaterial
fp = fp
temperature = T_fluid
pressure = pressure
[]
[ins_fv]
type = INSFVEnthalpyMaterial
temperature = 'T_fluid'
rho = ${rho}
[]
[]
[AuxKernels]
inactive = 'mixing_len'
[mixing_len]
type = WallDistanceMixingLengthAux
walls = 'top'
variable = mixing_length
execute_on = 'initial'
delta = 0.5
[]
[]
[Executioner]
type = Transient
solve_type = 'NEWTON'
petsc_options_iname = '-pc_type -pc_factor_shift_type'
petsc_options_value = 'lu NONZERO'
[TimeStepper]
type = IterationAdaptiveDT
dt = 1e-3
optimal_iterations = 6
[]
end_time = 15
nl_abs_tol = 1e-9
nl_max_its = 50
line_search = 'none'
automatic_scaling = true
off_diagonals_in_auto_scaling = true
compute_scaling_once = false
[]
[Outputs]
exodus = true
[]
(moose/modules/navier_stokes/test/tests/finite_volume/wcns/channel-flow/2d-transient.i)