One sometimes wants to run lattice Boltzmann simulations with more precision than is available in commonly supported floating point arithmetic. This is particularly true for confirming qualitative properties such as conservation laws. It is also true for GPUs where one may be restricted to 32b-bit floating point numbers. This talk presents a rescaling of the Skordos (1993) variable transformation to formulate a lattice Boltzmann scheme that can be implemented using integer arithmetic. In particular, 128-bit integer arithmetic is efficient on common hardware such as x86-64. Standard lattice Boltzmann schemes require division, while variants that target the Chorin artificial compressibility equations do not. The extra division comes at significant computational cost, even in floating point arithmetic, and is implemented using Newton's method in integer arithmetic.

Sharp and diffuse interface models are usually considered to be two fundamentally different approaches to the modeling of multiphase flows. In this contribution we discuss a conservative lattice Boltzmann phase field model as a phase separator and a momentum balance boundary condition forming a sharp interface. In this approach, the interaction between the two phases is limited to the nodes directly adjacent to the interface. This allows us to directly apply the super convergent cumulant lattice Boltzmann method in both domains and benefit from its excellent stability properties.

A convergence study of LB diffusion-interface method