View in EDS

An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations

Saved in:
Bibliographic Details
Title: An Explicit Meshless Point Collocation Solver for Incompressible Navier-Stokes Equations
Authors: George C. Bourantas, Benjamin F. Zwick, Grand R. Joldes, Vassilios C. Loukopoulos, Angus C. R. Tavner, Adam Wittek, Karol Miller
Source: Fluids, Vol 4, Iss 3, p 164 (2019)
Publisher Information: MDPI AG
Publication Year: 2019
Collection: Directory of Open Access Journals: DOAJ Articles
Subject Terms: transient incompressible Navier-Stokes, meshless point collocation method, stream function-vorticity formulation, strong form, explicit time integration, Thermodynamics, QC310.15-319, Descriptive and experimental mechanics, QC120-168.85
Description: We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.
Document Type: article in journal/newspaper
Language: English
Relation: https://www.mdpi.com/2311-5521/4/3/164; https://doaj.org/toc/2311-5521; https://doaj.org/article/2a4805e8e8f54234b9d63152220b1083
DOI: 10.3390/fluids4030164
Availability: https://doi.org/10.3390/fluids4030164
https://doaj.org/article/2a4805e8e8f54234b9d63152220b1083
Accession Number: edsbas.77F6352
Database: BASE
Description
Abstract:We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We discretize the governing equations using the Meshless Point Collocation (MPC) method. We compute the spatial derivatives that appear in the governing flow equations, using a novel interpolation meshless scheme, the Discretization Corrected Particle Strength Exchange (DC PSE). We verify the accuracy of the numerical scheme for commonly used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and unbounded flow past a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods. We estimate the stable time step using the Gershgorin circle theorem. The stable time step can be increased through the increase of the support domain of the weight function used in the DC PSE method.
DOI:10.3390/fluids4030164