A second-order volumetric boundary treatment for the lattice Boltzmann method

A new volumetric-type boundary treatment is introduced for the lattice Boltzmann method. Populations are projected onto a discontinuous piecewise linear basis and streamed using an exact geometrical mapping. The method is implemented in 2D for convex, stationary geometries. Stability is verified through a novel analysis tool based on the eigenvalues of the streaming operation. A convergence rate of $\geq2$ is achieved, indicating improved accuracy over precursor methods. For flow around a 2D airfoil, the method yields better lift and drag predictions.