Abstract:
Despite their cinematic appeal, turbulent flows involving fluid-solid coupling remain a computational challenge in animation. At the root of this current limitation is the numerical dispersion from which most accurate Navier-Stokes solvers suffer: proper coupling between fluid and solid often generates artificial dispersion in the form of local, parasitic trains of velocity oscillations, eventually leading to numerical instability. While successive improvements over the years have led to conservative and detail-preserving fluid integrators, the dispersive nature of these solvers is rarely discussed despite its dramatic impact on fluid-structure interaction. In this paper, we introduce a novel low-dissipation and low-dispersion fluid solver that can simulate two-way coupling in an efficient and scalable manner, even for turbulent flows. In sharp contrast with most current CG approaches, we construct our solver from a kinetic formulation of the flow derived from statistical mechanics. Unlike existing lattice Boltzmann solvers, our approach leverages high-order moment relaxations as a key to controlling both dissipation and dispersion of the resulting scheme. Moreover, we combine our new fluid solver with the immersed boundary method to easily handle fluid-solid coupling through time adaptive simulations. Our kinetic solver is highly parallelizable by nature, making it ideally suited for implementation on single- or multi-GPU computing platforms. Extensive comparisons with existing solvers on synthetic tests and real-life experiments are used to highlight the multiple advantages of our work over traditional and more recent approaches, in terms of accuracy, scalability, and efficiency.
