Unstructured lattice Boltzmann equation with memory

Starting from a second-order differential form of the semi-discrete Boltzmann equation, we construct a new finite-volume lattice Boltzmann equation on unstructured grids (ULBE). The new scheme (ULBE with memory) is demonstrated for the case of a Taylor-vortex flow and shown to produce stable and accurate results with time-step more than an order of magnitude above the standard LBE stability threshold.