HelloWorld-NavierStokes

Hello World to incompressible Navier--Stokes. The basic features of this solver are:

• Two-dimensional flow
• Second-order finite difference, staggered grid
• Fractional-step method
• Pressure-Poisson equation solved via FFTs
• OpenMP acceleration
• Fully explicit Euler time-integration
• Uniform grid spacing

Various branches have been created in what is (generally) increasing order of implementation complexity:

• main: Doubly-periodic domain, Pressure-Poisson equation solved via 2D FFTs
• walls: Implementation of wall-boundary conditions in one direction. The Poisson equation is solved with 1D FFTs in the periodic x-direction and a tridiagonal inversion in the remaining wall-normal direction. A scalar field is also added so that 2D Rayleigh-Benard flow can be simulated.
• implicit: Implicit time-stepping treatment of the diffusive terms using an Alternating Direct Implicit (ADI) approach or Helmholtz solver.
• RK3: Implementation of RK3 sub-stepping. Wall-normal viscous terms are always treated implicitly, while an option is available to treat the wall-parallel terms implicitly.
• non-uniform-grid: Grid-stretching in the wall-normal direction.
• 3d: Full 3D Navier--Stokes, with a standard channel geometry configuration. Periodicity in xy and wall-normal grid-stretching in z. WIP

Fields are dumped as binary files. In the later branches, I have routines which dump additional XDMF instructions such that they can be conveniently imported into Paraview.

Dependencies

• FFTW3
• Fortran compiler
• OpenMP

Acknowledgements

• Dr. Naoki Hori for his overall guidance in kick-starting this project
• My PhD advisor A/Prof. Daniel Chung, of which I have used his code as a reference for various intricacies related to incompressible flow solvers
• The contributors to AFiD, which I have also used as a reference