Abstract
AbstractComputational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. However, the simulation of turbulent flows in complex geometries is a compute-power intensive task due to the vast vector dimensions required by discretized meshes. We present a complete and self-consistent full-stack method to solve incompressible fluids with memory and run time scaling logarithmically in the mesh size. Our framework is based on matrix-product states, a compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without passing through the expensive dense-vector representation. This framework lays the foundation for a generation of more efficient solvers of real-life fluid problems.
Publisher
Springer Science and Business Media LLC
Reference50 articles.
1. Fefferman, C. L. Existence and smoothness of the Navier-Stokes equation. Millennium Prize Probl. 57, 67 (2000).
2. Orszag, S. A. & Patterson Jr, G. Numerical simulation of three-dimensional homogeneous isotropic turbulence. Phys. Rev. Lett. 28, 76 (1972).
3. Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk. SSSR, 30, 301–303 (1941).
4. Pope, S. B.Turbulent Flows (Cambridge University Press, New York, 2000).
5. Eisert, J., Cramer, M. & Plenio, M. B. Colloquium: Area laws for the entanglement entropy. Rev. Mod. Phys. 82, 277 (2010).