### What is it Appealing method for simulation of fluid flows - A competitive numerical tool for simulating fluid flows over a wide range of complex physical problems - LBMs were initially derived from **lattice gas cellular automata (LGCA).** The basic idea of LGCA is to *simulate the macroscopic behavior of a fluid flow* by implementing an extremely simplified model of the microscopic interactions between particles. - LBMs were developed, starting from LGCA, in the attempt to overcome their major drawbacks: - statistical noise, - increasing complexity of the collision operator (for three dimensional problems), - high viscosity (due to small number of collisions) - Nowadays, LBM has consolidated into a powerful alternative to more classical computational fluid dynamics models based on the *discretization of the Navier-Stokes equations of continuum mechanics.* ### Challenges & New ideas Applicability of the traditional Lattice Boltzman method to **uniform, regaular lattices** is restricted by the** intrinsic coupling of momentum and space discretization**. This is often disadvantageous in practice. **Available off-lattice Boltzmann algorithms** have *stability problems* which are to be *handled at the expense of additional computational cost.* > A **general characteristic-based algorithm** for off-lattice Boltzmann simulations that preserves all appealing properties of the standard Lattice Boltzmann method while **extending the method to unstructured grids.** > > Both, **finite-element and finite-difference implementations** of the algorithms are exemplified. Applications: 1. Particulate Fluid Simulation 2. Multi-component flows 3. Radiative Transport 4. Thermal Fluid Flows 5. Turbulence Simulations 6. Flows in Complex Geometries --- Magnus Performance Results: MLUPps (**M**ega **L**attice **UP**dates per **p**rocessing unit and **s**econd) as a function of cores