Boundary condition

Algorithm

The following describes the flow of logic in setting the boundary conditions.

In drive1.f:

• nek_advance(): single timestep if Pn/Pn-2

  • igeom=1: RHS terms

  • igeom=2: Actual

  • call heat

  • call fluid -> drive2.f

• fluid():

  • iftran=1,ifrich=0 -> plan3() in planx.f

• plan3(): Helmholtz operator split into two steps igeom=1,2

  • makef() : extrapolate pressure, solve for intermadiate velocity

  • solve for update of pressure, velocity divergence free. Only approximate operator is used here, because the exact one requires Helmholtz operator.

  • Block LU decomposition -> Consistent Helmholtz operator

  • Boundary condition is not required for the second step. Preconditioner.

  • See Blair Perot (1993)

Also if igeom=2:

• sethlm: h1=diffusion h2=helmholtz operator

• cresvif() compute residual:

  • lagvel, save velocity field

  • bcdirvc: boundary dirichlet velocity, bcneutr: boundary neutral -> bdry.f

  • opgradt: extrapolate pressire in time

  • add residual

• ophinv, opadd2: inverse helmholtz

• incomprn():

  • Project velocity

  • opgradt: pressure

  • opbinv -> navier1:

    • bdry?

    • opmask: set 0 to dirichlet BC, masked from the update

Boundary conditions

Periodicity: node numbering

bcdirvc

• CB = V (Constant Dirichlet in rea file)

• CB = v (user provided Dirichlet in userbc):

  • FACEIV: works on temporary arrays tmp1, tmpr3

    • facind: face index

    • facev -> userbc

    • opdsop: max min, to get consistent bc shared nodes

    • if not stress forulation ifstrs:

      • add2 -> Velocity + Tmp

bcneutr: Neumann transient?

No mask

• chkcbc: alignment check

• SYM <- called bcmask <->= nek_init modifies the masking for one component

• Also by sethmsk

• b1mask, b2mask, b3mask arrays:

• FEM trick, if you don’t anything: Natural BC. Normal stresses are 0, BC is the fluxes on the last element.

subs2.f

• sh: faceiv -> sets traction array TRX, TRY, TRZ -> as acceleration

• faccvs -> multiplies by the surface area -> force

• globrot, does rotation with respect to global coordinates

• added to RHS: bfx, bfy -> acceleration

Velocity should be v=0

Caution: Pressure preconditioner BC are related

To Do

Set velocity v=0, normal component of velocity is zero, opposite of on boundary condition.

FAQ

Time-stepping algebra

Mass matrix requires time levels (n, n-1, n-2): extrapolated Conv / Stiffness requires time levels (n-1, n-2): explicit

Comparison with Adams-Bashforth

AB2: needs previous RHS BDF: needs previous LHS

Why not: Runge-Kutta?

According to mathematicians, it is not clear because you have a pressure correction in each sub-step.

CFL number

BDF3/EXT3: CFL=0.6. Characteristic emthod