Jongsu Liam Kim | Blog

# Navier Stokes Equation Solver for Homogeneous Isotropic Turbulence

17 Jul 2017(This content is originally written by Kyongmin Yeo’s manual)

# Introduction

The spectral method is solving certain differential equation by some “basis function”, typically sinusoids with Fourier method. With the Navier-Stokes equation, it can remove presssure term in N-S equation and solve viscous term analytically.

Pros:

- Removing pressure term is huge performance advantage
- Accurate result because differential operator doesn’t depends on grid size

Cons:

- Only can be applied to periodic domain

# Governing Equation

## Navier-Stokes equation to rotational form

Original Navier-Stokes equation in **convection form** is

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