ICTS

The Lattice Boltzmann Method (LBM), with its simplified kinetic descriptions, has emerged as an important tool for simulating hydrodynamics. Using LBM as an example, I will argue that the second law of thermodynamics in discrete space-time an provides a new way to formulate non-linearly stable numerical numerical methods for hydrodynamics. I will provide exact solution for discrete time  H-theorem and use it to build next generation entropic LBM, where non-linear stability is achieved without compromising on the simplicity of standard LBM. Finally, I will also argue that the Body Centered Cubic  arrangement of grid points  provides a more natural set-up for formulating LBM. Using these improvements, I will illustrate an order-of-magnitude gain in efficiency for LBM and thus a significant progress towards feasibility of Direct numerical simulation for realistic flows.