Approximation viscosity of one-parameter families of lattice Boltzmann equations

A number of properties of parametric lattice Boltzmann schemes are considered. The Chapman-Enskog method is used to derive a system of equations for hydrodynamic variables and to obtain an expression for the approximation viscosity from the differential approximation of the schemes. It is shown that there exists the numerical viscosity that should be taken into account during numerical computations. Necessary stability conditions are obtained from the nonnegativity condition for the approximation viscosity. The possibility of computations using the proposed schemes is demonstrated by the numerical solution of the lid-driven cavity flow problem when the standard lattice Boltzmann equation is inapplicable.