A three-dimensional multispeed thermal model of the finite difference lattice Boltzmann method (FDLBM) is proposed. In the FDLBM we can select particle velocities independently from the lattice configuration. Particle velocities of the proposed model consist of vectors pointing to the vertex...

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N-component Cahn–Hilliard system modeling the phase separation of an N-component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate...

We consider an unconditionally gradient stable scheme for solving the Allen–Cahn equation representing a model for anti-phase domain coarsening in a binary mixture. The continuous problem has a decreasing total energy. We show the same property for the corresponding discrete problem by using...

The current finite difference lattice Boltzmann method (FDLBM) gives a fixed specific heat ratio because internal energy is limited to the translational freedom of the space. Yan et al. and Kataoka et al. clarified the conditions for deriving models with arbitrary specific heat ratio and...

We consider a second-order conservative nonlinear numerical scheme for the N-component Cahn–Hilliard system modeling the phase separation of a N-component mixture. The scheme is based on a Crank–Nicolson finite-difference method and is solved by an efficient and accurate nonlinear multigrid...