Jongsu Liam Kim | Blog

# Navier Stokes Equation Solver for Homogeneous Isotropic Turbulence

(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

Original Navier-Stokes equation in convection form is

\[\begin{align} \dfrac{\partial u_i}{\partial t} &= -\dfrac{\nabla p}{\rho} - (u...