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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.
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