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Local Bases for Model‐reduced Smoke Simulations
Author(s) -
Mercier Olivier,
Nowrouzezahrai Derek
Publication year - 2020
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13908
Subject(s) - basis (linear algebra) , computer science , overhead (engineering) , simple (philosophy) , basis function , vector field , algorithm , projection (relational algebra) , flow (mathematics) , domain (mathematical analysis) , heuristic , reduction (mathematics) , computational science , mathematical optimization , topology (electrical circuits) , geometry , artificial intelligence , mathematics , mathematical analysis , philosophy , epistemology , operating system , combinatorics
Abstract We present a flexible model reduction method for simulating incompressible fluids. We derive a novel vector field basis composed of localized basis flows which have simple analytic forms and can be tiled on regular lattices, avoiding the use of complicated data structures or neighborhood queries. Local basis flow interactions can be precomputed and reused to simulate fluid dynamics on any simulation domain without additional overhead. We introduce heuristic simulation dynamics tailored to our basis and derived from a projection of the Navier‐Stokes equations to produce physically plausible motion, exposing intuitive parameters to control energy distribution across scales. Our basis can adapt to curved simulation boundaries, can be coupled with dynamic obstacles, and offers simple adjustable trade‐offs between speed and visual resolution.