A weighted meshfree collocation method for incompressible flows using radial basis functions

A weighted strong form collocation method using radial basis functions and explicit time integration is proposed to solve the incompressible Navier-Stokes equations. The velocities and pressure are solved directly at the same time step and the continuity equation is satisfied at each time step which...

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Bibliographic Details
Published in:Journal of computational physics Vol. 401; p. 108964
Main Authors: Wang, Lihua, Qian, Zhihao, Zhou, Yueting, Peng, Yongbo
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 15.01.2020
Elsevier Science Ltd
Subjects:
Boundary conditions
Collocation methods
Compressibility
Computational fluid dynamics
Computational physics
Continuity equation
Explicit time integration
Flow control
Fluid flow
Free surfaces
Incompressible flow
Incompressible Navier-Stokes equations
Meshless methods
Optimal convergence
Pressure oscillations
Radial basis function
Radial basis functions
Stability analysis
Strong form collocation
Time integration
Radial basis functions
Optimal convergence
Stability analysis
Incompressible Navier-Stokes equations
Explicit time integration
Strong form collocation
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:A weighted strong form collocation method using radial basis functions and explicit time integration is proposed to solve the incompressible Navier-Stokes equations. The velocities and pressure are solved directly at the same time step and the continuity equation is satisfied at each time step which improve the solution accuracy and stability. No artificial compressibility coefficient needs to be introduced for modeling the incompressible flows and no pressure oscillation arises in the numerical solutions. Optimal convergence can be achieved by imposing the derived proper weights on the boundaries and the continuity equation. Radial basis collocation method in a Lagrangian form is quite easy to capture the moving boundary or free surface in flow problems. Moreover, solid boundary conditions can be enforced directly and no special treatments are required. Further, critical time step for the explicit time integration is predicted in the stability analysis and the influences on the stability are evaluated. Numerical studies validate the high accuracy as well as good stability of the presented method. •A weighted collocation method is raised for incompressible Navier-Stokes equations.•Optimal convergence can be gained by imposing the proper weights on the boundaries.•No artificial compressibility coefficient is used to model the incompressible flow.•No pressure oscillation arises in the numerical solutions.•It's quite easy to capture the moving boundary or free surface in flow problems.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2019.108964