Examples

The repository contains runnable example scripts under examples/.

Run from repository root:

julia --project=. examples/gaussian_nobody_convergence.jl
julia --project=. examples/gaussian_outside_circle.jl
julia --project=. examples/moving_mono_nobody_mms_convergence.jl
julia --project=. examples/moving_diph_planar_interface_mms_convergence.jl

Available examples

• examples/gaussian_nobody_convergence.jl

  • 2D no-body (full domain), periodic boundaries.
  • Advects and diffuses a Gaussian with known analytical solution.
  • Uses solve_unsteady!(...; scheme=:CN) and reports observed convergence order.

• examples/gaussian_outside_circle.jl

  • 2D outside a circular embedded body with rotational velocity field.
  • Periodic box + interface Robin condition Robin(0, 1, 0).
  • Advances with backward Euler and tracks total scalar mass drift.
  • Writes gaussian_outside_circle_mass.csv.

• examples/embedded_wall_hot_cylinder.jl

  • Embedded fixed wall with advection-diffusion coupling.
  • Demonstrates mixed model BC handling and interface diffusion law.

• examples/diph_planar_interface_constant_jump.jl

  • Fixed diphasic planar interface.
  • Uses InterfaceConditions for scalar/flux coupling.

• examples/diph_planar_interface_mms.jl

  • Fixed diphasic MMS benchmark.
  • Reports refinement errors and observed order.

• examples/moving_mono_nobody_mms_convergence.jl

  • Moving-model path without embedded interface (body=-1).
  • Verifies moving mono assembly convergence in periodic box.

• examples/moving_diph_planar_interface_mms_convergence.jl

  • Moving diphasic planar interface MMS.
  • Verifies robust convergence with translating interface.

• examples/moving_static_recovery_compare.jl

  • Compares fixed vs moving (with static interface, wγ=0) final states.
  • Prints L2, L∞, and max-abs differences.

• examples/coupled_darcy_advdiff_oneway_1d.jl

  • First real one-way coupling: Darcy velocity drives advection-diffusion.
  • Uses OneWayCoupling with CouplingMap(:darcy, :transport, :velocity).
  • Compares coupled result to direct velocity injection reference.

• examples/coupled_darcy_advdiff_twoway_1d.jl

  • First real two-way coupling: concentration feeds back to Darcy mobility.
  • Uses TwoWayCoupling with outer Picard iterations and relaxation.
  • Includes map CouplingMap(:transport, :darcy, :concentration).

First coupled workflow notes

• One-way: flow drives scalar transport.
• Two-way: scalar updates mobility λ(c), which updates flow, which updates scalar.
• SolverCore handles orchestration only; wrappers expose coupling fields.
• Current Darcy unsteady hook is quasi-steady per transport time step.

Tests

Run the package test suite with:

julia --project=. -e 'using Pkg; Pkg.test()'

Current tests cover:

• no-body Gaussian convergence under periodic flow (:CN),
• outside-circle rotating-flow case with mass-drift bound,
• moving static-geometry recovery vs fixed (mono and diph),
• moving zero-advection reduction to PenguinDiffusion (mono and diph),
• moving MMS checks (mono and diph).

MMS matrix sweep:

julia --project=. test/test_mms_matrix_report.jl

Validated orders (2026-03-13):