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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

RBF Liquids: An Adaptive PIC Solver Using RBF-FD

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Nakanishi, Rafael [1] ; Nascimento, Filipe [1] ; Campos, Rafael [1] ; Pagliosa, Paulo [2] ; Paiva, Afonso [1]
Total Authors: 5
[1] Univ Sao Paulo, ICMC, BR-13566590 Sao Carlos, SP - Brazil
[2] Univ Fed Mato Grosso do Sul, FACOM, Campo Grande, MS - Brazil
Total Affiliations: 2
Document type: Journal article
Source: ACM TRANSACTIONS ON GRAPHICS; v. 39, n. 6 DEC 2020.
Web of Science Citations: 0

We introduce a novel liquid simulation approach that combines a spatially adaptive pressure projection solver with the Particle-in-Cell (PIC) method. The solver relies on a generalized version of the Finite Difference (FD) method to approximate the pressure field and its gradients in tree-based grid discretizations, possibly non-graded. In our approach, FD stencils are computed by using meshfree interpolations provided by a variant of Radial Basis Function (RBF), known as RBF-Finite-Difference (RBF-FD). This meshfree version of the FD produces differentiation weights on scattered nodes with high-order accuracy. Our method adapts a quadtree/octree dynamically in a narrow-band around the liquid interface, providing an adaptive particle sampling for the PIC advection step. Furthermore, RBF affords an accurate scheme for velocity transfer between the grid and particles, keeping the system's stability and avoiding numerical dissipation. We also present a data structure that connects the spatial subdivision of a quadtree/octree with the topology of its corresponding dual-graph. Our data structure makes the setup of stencils straightforward, allowing its updating without the need to rebuild it from scratch at each time-step. We show the effectiveness and accuracy of our solver by simulating incompressible inviscid fluids and comparing results with regular PIC-based solvers available in the literature. (AU)

FAPESP's process: 18/06145-4 - Digital animation of powder snow avalanches
Grantee:Filipe de Carvalho Nascimento
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 19/23215-9 - Meshfree methods based on generalized finite differences using MLS and SPH
Grantee:Afonso Paiva Neto
Support Opportunities: Regular Research Grants