Finite difference solver with 5th-order WENO method for two-phase Rayleigh-Taylor fluid instability
The C codes (for computation) and MATLAB code (for posttreatment) are pasted here. 
Open source codes
Practical tutorial and numerical implementation of multi-phase flow simulation based on phase-field model
The tutorial, C and Matlab codes of multi-phase fluid mixing in a tilted channel. The C code (for computation) and Matlab code (for post-treatment) are pasted here. 
C and MATLAB codes: Phase-field method for 3D volume reconstruction
This is phase-field model of 3D volume reconstruction of a teapot. The finite difference method is used to implement the spatial discretization. An energy-stable second-order linear scheme is used to perform temporal approximation. The C code is used to implement numerical calculation. The MATLAB codes are used for pre- and post-treatments. 
MATLAB code: Fourier spectral method for 2D Cahn-Hilliard equation
This is a simple and practical solver (Fourier spectral method) for 2D Cahn-Hilliard equation with periodic boundary conditions. The MATLAB codes are pasted here. 
MATLAB code: Lattice Boltzmann method (D2Q9) for 2D Cahn-Hilliard equation
This is a simple Lattice Boltzmann solver for 2D Cahn-Hilliard equation. The MATLAB codes are pasted here. 
MATLAB code: Lattice Boltzmann method (D2Q9) for fluid flow passing through obstacles
This is a simple Lattice Boltzmann solver for 2D fluid flow passing through solid obstacles. The MATLAB codes are pasted here. 
MATLAB code: Third-order Runge-Kutta Fourier spectral method for phase-field crystal model with FCC ordering structure
This is a mass-conserved Fourier spectral solver for phase-field crystal model with FCC ordering structure. Third-order Runge-Kutta scheme is used to update solution. The MATLAB codes are pasted here. 
MATLAB code: Explicit finite difference method for phase-field dendritic growth model
This is a totally explicit solver for phase-field dendritic growth model. The spatial discretization is performed based on finite difference method. The MATLAB codes are pasted here. 
MATLAB code: Explicit finite difference method for Image Segmentation
This is an explicit finite difference solver for a phase-field model of image segmentation. The MATLAB codes are pasted here. 
MATLAB code: Fourier spectral method for Molecular Beam Epitaxy (MBE) model
This is a Fourier spectral solver for Molecular Beam Epitaxy (MBE) model. The MATLAB codes are pasted here. 
MATLAB code: Energy-stable linear convex splitting method for the Quasi-crystal pattern
This is a numerical method for the generation of Quasi-crystal pattern. The Fourier spectral method is used to implement spatial discretization. The time-marching scheme is designed based on a linear and unconditionally energy-stable Runge-Kutta convex splitting method. The MATLAB codes are pasted here. 
MATLAB code: Lattice Boltzmann method (D2Q9) for binary phase-field surfactant model
This is a simple Lattice Boltzmann solver (D2Q9) for simulating binary phase-field surfactant dynamics. The MATLAB codes are pasted here. 
C computation code and MATLAB posttreatment code: Immersed Boundary Method for fluid flows passing through a cylinder
This is a finite difference Immersed Boundary Method (IBM) code for simulating 2D flow passing through a cylinder. The C and MATLAB codes are pasted here. 
MATLAB code: Finite difference projection method for 2D incompressible Navier-Stokes equations
This is a simple projection solver for 2D Navier-Stokes equations. The finite difference method is used for spatial discretization. The lid-driven cavity flow is simulated. The MATLAB codes are pasted here. 
MATLAB code: Lattice Boltzmann method (D2Q9) for fluid flow with heat transfer
This is a simple Lattice Boltzmann solver for fluid flow with heat transfer (natural convection). The MATLAB codes are pasted here. 