maximum number of scalars solutions of an advection equation, apart from the variables of the turbulence model ) , that is to say the temperature and other scalars (passive or not, user-defined or not)
Error estimator for Navier-Stokes. iest = iespre: prediction, (default name: EsPre). After the velocity prediction step (yielding ), the estimator , local variable calculated at every cell , is created from , which represents the residual of the equation solved during this step: and :
Error estimator for Navier-Stokes. iest = iesder: drift (default name: EsDer). The estimator is based on the following quantity (intrinsic to the code):
Error estimator for Navier-Stokes. iest = iescor: correction, (default name: EsCor). The estimator comes directly from the mass flow calculated with the updated velocity field:
Error estimator for Navier-Stokes. iest = iestot: total, (default name: EsTot). The estimator , local variable calculated at every cell , is based on the quantity , which represents the residual of the equation using the updated values of and :
if itypfb=i_convective_inlet: inlet face where the total mass flux is prescribed.
Zero-flux condition for pressure and Dirichlet condition for all other variables. The value of the Dirichlet must be given in rcodcl(ifac,ivar,1) for every value of ivar, except for ivar = ipr. The other values of rcodcl and icodcl are filled automatically. The diffusive flux is CANCELLED (therefore the total mass flux is due to convection only).
Zero-flux condition for pressure and Dirichlet condition for all other variables. The value of the Dirichlet must be given in rcodcl(ifac,ivar,1) for every value of ivar, except for ivar = ipr. The other values of rcodcl and icodcl are filled automatically.
if itypfb=iephcf: mixed inlet for compressible flow with given total pressure and total enthalpy (reservoir boundary conditions).
Boundary values are obtained by solving a Riemann problem between an inner (values at boundary cells center) and an outer state.
Homogeneous Neumann boundary condition for the pressure (seen by the reconstruction gradients and the diffusion operator).
Dirichlet (icodcl=1) for velocity and total energy.
Analytical boundary convective fluxes of momentum and total energy are computed. Note that the pressure boundary value is needed to compute those two fluxes (seen by the pressure gradient of the momentum equation).
If the mass flow is coming in, Dirichlet condition for the scalars and the turbulent quantities is used (or zero-flux condition if no Dirichlet value has been specified).
If the mass flow is going out, zero-flux condition are set for the scalars and the turbulent quantities.
Error estimator for Navier-Stokes. iest = iescor: correction, (default name: EsCor). The estimator comes directly from the mass flow calculated with the updated velocity field:
The velocities are taken at the cell centers, the divergence is calculated after projection on the faces. represents the Kronecker symbol.
The first family, k=1, is the absolute raw value of the divergence of the mass flow The second family, $k=2$, represents a physical property and allows to evaluate the difference in .
Ideally, it is equal to zero when the Poisson equation is solved exactly and the projection from the mass flux at the faces to the velocity at the cell centers is made in a set of functions with null divergence.
Error estimator for Navier-Stokes. iest = iesder: drift (default name: EsDer). The estimator is based on the following quantity (intrinsic to the code):
Ideally, it is equal to zero when the Poisson equation related to the pressure is solved exactly. minus the mass source term.
if itypfb=iesicf: imposed inlet/outlet for compressible flow (for example, supersonic inlet).
A boundary value has to be given for the following quantities:
velocity
two of the four thermodynamical properties: density, pressure, total energy, temperature
all other variables.
Homogeneous Neumann boundary condition for the pressure (seen by the reconstruction gradients and the diffusion operator).
Dirichlet condition for the velocity and the total energy.
The boundary convective fluxes of momentum and total energy are computed from a Rusanov scheme for stability reasons. Note that the pressure boundary value is needed to compute those two fluxes (seen by the pressure gradient of the momentum equation).
If the mass flow is coming in, Dirichlet condition for the scalars and the turbulent quantities is used (or zero-flux condition if no Dirichlet value has been specified).
If the mass flow is going out, zero-flux condition are set for the scalars and the turbulent quantities.
Error estimator for Navier-Stokes. iest = iespre: prediction, (default name: EsPre). After the velocity prediction step (yielding ), the estimator , local variable calculated at every cell , is created from , which represents the residual of the equation solved during this step: and :
By definition:
The first family, k=1, suppresses the volume which intrinsicly appears with the norm .
The second family, k=2, exactly represents the norm . The size of the cell therefore appears in its calculation and induces a weighting effect.
is ideally equal to zero when the reconstruction methods are perfect and the associated system is solved exactly.
Error estimator for Navier-Stokes. iest = iestot: total, (default name: EsTot). The estimator , local variable calculated at every cell , is based on the quantity , which represents the residual of the equation using the updated values of and :
By definition:
The mass flux in the convective term is recalculated from expressed at the cell centers (and not taken from the updated mass flow at the faces).
As for the prediction estimator:
The first family, k=1, suppresses the volume which intrinsicly appears with the norm .
The second family, k=2, exactly represents the norm . The size of the cell therefore appears in its calculation and induces a weighting effect.
if itypfb=isolib: free outlet face (or more precisely free inlet/outlet with forced pressure)
The pressure is always treated with a Dirichlet condition, calculated with the constraint . The pressure is set to at the first isolib face met. The pressure calibration is always done on a single face, even if there are several outlets.
if the mass flow is coming in, the velocity is set to zero and a Dirichlet condition for the scalars and the turbulent quantities is used (or zero-flux condition if no Dirichlet value has been specified).
if the mass flow is going out, zero-flux condition are set for the velocity, the scalars and the turbulent quantities.
Nothing is written in icodcl or rcodcl for the pressure or the velocity. An optional Dirichlet condition can be specified for the scalars and turbulent quantities.
Remarks
A standard isolib outlet face amounts to a Dirichlet condition (icodcl=1) for the pressure, a free outlet condition (icodcl=9) for the velocity and a Dirichlet condition (icodcl=1) if the user has specified a Dirichlet value or a zero-flux condition (icodcl=3) for the other variables.
if itypfb=isopcf: mixed outlet for compressible flow with a given pressure.
Boundary values are obtained by solving a Riemann problem between an inner (values at boundary cells center) and an outer state. The given pressure is considered as an outer value.
Homogeneous Neumann boundary condition for the pressure (seen by the reconstruction gradients and the diffusion operator).
Dirichlet (icodcl=1) for the velocity and the total energy.
Analytical boundary convective fluxes of momentum and total energy are computed. Note that the pressure boundary value is needed to compute those two fluxes. (seen by the pressure gradient of the momentum equation).
If the mass flow is coming in, Dirichlet condition for the scalars and the turbulent quantities is used (or zero-flux condition if no Dirichlet value has been specified).
If the mass flow is going out, zero-flux condition are set for the scalars and the turbulent quantities.
if itypfb=isspcf: supersonic outlet for compressible flow.
Nothing needs to be given. The imposed state at the boundary is the upstream state (values in boundary cells).
Homogeneous Neumann boundary condition for the pressure (seen by the reconstruction gradients and the diffusion operator).
Dirichlet (icodcl=1) for the velocity and the total energy. (pressure boundary value seen by the pressure gradient of the momentum equation).
If the mass flow is coming in, Dirichlet condition for the scalars and the turbulent quantities is used (or zero-flux condition if no Dirichlet value has been specified).
If the mass flow is going out, zero-flux condition are set for the scalars and the turbulent quantities.
boundary condition type for mesh velocity in ALE: imposed velocity.
In the case where all the nodes of a face have a imposed displacement, it is not necessary to fill the tables with boundary conditions mesh velocity for this face, they will be erased. In the other case, the value of the Dirichlet must be given in rcodcl(ifac,ivar,1) for every value of ivar (iuma, ivma and iwma). The other boxes of rcodcl and icodcl are completed automatically. The tangential mesh velocity is taken like a tape speed under the boundary conditions of wall for the fluid, except if wall fluid velocity was specified by the user in the interface or cs_user_boundary_conditions (in which case it is this speed which is considered).
maximum number of scalars solutions of an advection equation, apart from the variables of the turbulence model ) , that is to say the temperature and other scalars (passive or not, user-defined or not)