Boundary Conditions (BC)

Boundary Conditions (BC)#

Boundary nodes are those in the immediate vicinity of a numerical boundary. Since there are a number of populations on a boundary node, but only a few macroscopic quantities with physical sense over the boundary, the definition of boundary conditions (BCs) in LBM requires intuition on mesoscopic level.

Some BCs are directly applied with the populations and we assume the boundaries to sit on the links between nodes (it’s safe to assume they’re on the middle).

We also employ regularized BCs, which consist on the recustruction of populations through macroscopics and to which the nodes position coincide with the boundaries.

Important

We fix all particular cases (edges and corners) by imposing an overwriting order. From first to last:

SLIP (z) \(\Rightarrow\) SLIP (y) and WALL (y) \(\Rightarrow\) OUTLET and INLET

To know more about this order and its impact, check BC order validation test

The applications of the implemented boundary conditions are listed below:

  • Solid Wall
    • Halfway Bounce-Back:

      • Advantages: Has second-order accuracy and is completely local.

      • Disavantages: Boundary location does not coincide with node and has a relaxation time dependance.

    • Regularized HWBB:

      • Advantages: Boundary is located at the node and has increased stability.

      • Disavantages: Uses non-local values.

  • Moving Wall
    • Velocity Bounce-Back:

      • Advantages: Has second-order accuracy and is completely local.

      • Disavantages: Increases average domain density, which can lead to instabilities.

  • Free Surface
    • Regularized Neumann (Slip):

      • Advantages: High stability and is completely local.

      • Disavantages: Requires some considerations which are simplifications of a real case.

  • Inlet
    • Anti Bounce-Back:

      • Advantages: Fully local.

      • Disavantages: Presents some stability issues.

    • Velocity Bounce-Back:

      • Advantages: Has second-order accuracy and is completely local.

      • Disavantages: Increases average domain density, which can lead to instabilities.

    • Uniform Velocity:

      • Advantages: Does not increase the simulation average density.

      • Disavantages: Has to operate with constant density.

    • Pops Reconstruction:

      • Advantages: Allows for a turbulent flow inlet, saving computational memory.

      • Disavantages: Requires a sufficient domain length to assure stability.

    • Synthetic Eddy Method:

      • Advantages: Is able to recriate an average velocity profile preserving a turbulent intensity.

      • Disavantages: It requires a extensive input which includes a Reynolds stress tensor.

  • Outlet
    • Anti Bounce-Back:

      • Advantages: Fully local and keeps a stable pressure.

      • Disavantages: Presents some stability issues which may cause simulation to diverge.

    • Neumann:

      • Advantages: Fully local and has a flexible density.

      • Disavantages: Does not assure a stability on domain’s average density.

    • Regularized Neumann (Outlet):

      • Advantages: Assure a stable average density of computational domain.

      • Disavantages: Has to be positioned sufficiently far from regions of high pressure gradient.