3D Navier Stokes Equation Solver

Solving 3D incompressible Navier Stokes equation using finite difference method with uniform grid in parallel. The incompressibility is implemented using pressure-corr
ection scheme and linear (Poisson) solver is implemented using multigrid v-cycle.

The code is pretty much based on this MATLAB implementation. The documentation is [here](http://math.mit.edu/c\ se/codes/mit18086_navierstokes.pdf).

Problem Statement

Incompressible Navier Stokes Equation:

Incompressibility condition:

3D cubic domain [0,1]^3.

Dicirhlet boundary conditions for veocities and Neumann boundary condition for pressure are implemented. The velocity on the boundary can be specified in double bcs[3][6] array (first dimension specifies x- y- z- velocity, second dimsension specifies the face of the cube).

Implementation

1. The cubic domain is discretized by unform staggered grid.
2. The partial differential equations are discretized using finite difference method.
3. Parallelization is implemented by OpenMP.
4. Pressure-correction scheme is used to enforce incompressibility.

Usage

./multigrid [# of threads] [max level of v-cycle] [x-grid size] [y-grid size] [z-grid size]