Meshfree methods based on generalized finite differences using MLS and SPH

• Grant number: 19/23215-9
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2020
• End date: October 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Computer Science
• Principal Investigator: Afonso Paiva Neto
• Grantee: Afonso Paiva Neto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Smoothed Particle Hydrodynamics (SPH) is one of the most popular meshless methods in computational fluid dynamics. Since its conception, it has been the object of study by researchers who seek to improve the method and apply it to solve various problems. One of the most significant improvements was proposed by Dilts [Dil98], which presents a way to combine the SPH approach with Moving Least Squares (MLS) to improve the accuracy and stability of the traditional SPH method. Despite the quality of the results produced, Dilts' Moving Least Squares Hydrodynamics (MLSPH) method still suffers from its high computational cost due to the way differential operators are calculated. In this project, we propose a new robust and efficient meshless method combining the simplicity of the Finite Difference Method with the accuracy of the MLSPH method and other meshless methods. Besides, we intend to explore the vast amount of applications of the proposed new method called MLPSH-FD in problems related to Computer Graphics and Computational Physics. (AU)

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SILVA, SAMUEL ROCHA; VIEIRA, THALES; MARTINEZ, DIMAS; PAIVA, AFONSO. On novelty detection for multi-class classification using non-linear metric learning. EXPERT SYSTEMS WITH APPLICATIONS, v. 167, APR 1 2021. (19/23215-9)

OLIVEIRA, FELIPE; PAIVA, AFONSO. Narrow-Band Screen-Space Fluid Rendering. COMPUTER GRAPHICS FORUM, v. 41, n. 6, p. 12-pg., 2022-04-09. (13/07375-0, 19/23215-9)

DE FIGUEIREDO, LUIZ HENRIQUE; PAIVA, AFONSO. Region reconstruction with the sphere-of-influence diagram. COMPUTERS & GRAPHICS-UK, v. 107, p. 12-pg., 2022-08-26. (19/23215-9)

NAKANISHI, RAFAEL; NASCIMENTO, FILIPE; CAMPOS, RAFAEL; PAGLIOSA, PAULO; PAIVA, AFONSO. RBF Liquids: An Adaptive PIC Solver Using RBF-FD. ACM TRANSACTIONS ON GRAPHICS, v. 39, n. 6, DEC 2020. (18/06145-4, 19/23215-9)

INCAHUANACO, FILOMEN; PAIVA, AFONSO. Surface reconstruction method for particle-based fluids using discrete indicator functions. COMPUTERS & GRAPHICS-UK, v. 114, p. 10-pg., 2023-06-03. (19/23215-9, 13/07375-0)

QUISPE, FILOMEN INCAHUANACO; PAIVA, AFONSO; DECARVALHO, BM; GONCALVES, LMG. Counting Particles: a simple and fast surface reconstruction method for particle-based fluids. 2022 35TH SIBGRAPI CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI 2022), v. N/A, p. 5-pg., 2022-01-01. (19/23215-9, 13/07375-0)