Rectangular lattice Boltzmann method

A set of rectangular lattice Boltzmann methods for fluid flows is developed. It is shown that reformulating local equilibrium distribution functions can result in the rectangular lattice Boltzmann models without the aid of an interpolation for shallow water equations, Navier-Stokes equations, and axisymmetric flow equations. In addition, schemes for correct incorporation of force terms into the models are proposed for simulations of flows involving forces in practice. The methods completely retain the innate kinetic features and the simple procedure of the standard lattice Boltzmann method with an additional benefit of being suitable for rectangular lattices at little extra computational cost. The methodology is illustrated and validated through its application to different flow problems, demonstrating the potential power of the models.