This is a simple two-phase incompressible and immiscible fluid solver based on immersed boundary method (IBM). FFT is used to solve the Navier-Stokes equations. The MATLAB codes are pasted here. 
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. 
This is a simple Lattice Boltzmann solver (D2Q9) for simulating binary phase-field surfactant dynamics. The MATLAB codes are pasted here. 
This is a Fourier spectral solver for Molecular Beam Epitaxy (MBE) model. The MATLAB codes are pasted here. 
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. 
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. 
This is a simple Lattice Boltzmann solver for 2D Cahn-Hilliard equation. The MATLAB codes are pasted here. 
This is a simple Lattice Boltzmann solver for 2D fluid flow passing through solid obstacles. The MATLAB codes are pasted here. 
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. 
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. 
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. 
This is an explicit finite difference solver for a phase-field model of image segmentation. The MATLAB codes are pasted here. 
This is a simple Lattice Boltzmann solver for fluid flow with heat transfer (natural convection). The MATLAB codes are pasted here. 