In this work, we are concerned with the lattice Boltzmann method for anisotropic convection–diffusion equations (CDEs). We prove that the collision matrices of many widely used lattice Boltzmann models for such equations admit an elegant property, which guarantees the second-order accuracy of the half-way anti-bounce-back scheme. Numerical experiments validated our results for both two- and three-dimensional anisotropic CDEs.
- Anisotropic convection–diffusion equations
- Collision matrix
- Half-way anti-bounce-back scheme
- Lattice Boltzmann method
- Second-order accuracy