arXiv:1503.08360v1 [cs.NA] 28 Mar 2015 Do current lattice Boltzmann methods for diffusion-type equations respect maximum principles and the non-negative constraint? Authored by S. Karimi Graduate Student, University of Houston. K. B. Nakshatrala Department of Civil & Environmental Engineering University of Houston, Houston, Texas 77204–4003. phone: +1-713-743-4418, e-mail: knakshatrala@uh.edu website: http://www.cive.uh.edu/faculty/nakshatrala This figure shows that a popular multiple-relaxation-time lattice Boltzmann method violates the non-negative constraint for a transient diffusion equation. 2015 Computational & Applied Mechanics Laboratory