Implementation of boundary conditions for meshless methods

Frank C. Günther; Wing Kam Liu

doi:10.1016/S0045-7825(98)00014-0

Implementation of boundary conditions for meshless methods

Frank C. Günther, Wing Kam Liu^*

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

144 Scopus citations

Abstract

Boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite-element-like Kronecker delta condition. Furthermore, it is frequently desirable, especially in fluid mechanics, to impose general, nonlinear boundary and interface constraints. This paper describes a computationally efficient algorithm based on d'Alembert's principle that can be used for general constraints both in meshless methods and finite elements. First, a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed. Subsequently, an analogous method is developed for nonlinear constraints. Special attention is given to imposing general boundary and fluid - structure interface conditions on the Navier-Stokes equations in terms of conservative variables. Numerical results using d'Alembert's principle with the Reproducing Kernel Particle Method (RKPM), including viscous, supersonic flow past a NACA 7012 airfoil, are shown.

Original language	English (US)
Pages (from-to)	205-230
Number of pages	26
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	163
Issue number	1-4
DOIs	https://doi.org/10.1016/S0045-7825(98)00014-0
State	Published - Sep 21 1998

Funding

The support of this researchb y the Air Force Office of Scientific Research (AFOSR), the Office of Naval Research (ONR), and the National Science Foundation (NSF) is gratefully acknowledged. This work is sponsored in part by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement number DAAH04-952-0003/ contract number DAAH04-95-C-0008, the content of which does not necessarily reflect the position or the policy of the government, and no official endorsements hould be inferred.

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/S0045-7825(98)00014-0

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title = "Implementation of boundary conditions for meshless methods",

abstract = "Boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite-element-like Kronecker delta condition. Furthermore, it is frequently desirable, especially in fluid mechanics, to impose general, nonlinear boundary and interface constraints. This paper describes a computationally efficient algorithm based on d'Alembert's principle that can be used for general constraints both in meshless methods and finite elements. First, a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed. Subsequently, an analogous method is developed for nonlinear constraints. Special attention is given to imposing general boundary and fluid - structure interface conditions on the Navier-Stokes equations in terms of conservative variables. Numerical results using d'Alembert's principle with the Reproducing Kernel Particle Method (RKPM), including viscous, supersonic flow past a NACA 7012 airfoil, are shown.",

author = "G{\"u}nther, {Frank C.} and Liu, {Wing Kam}",

note = "Funding Information: The support of this researchb y the Air Force Office of Scientific Research (AFOSR), the Office of Naval Research (ONR), and the National Science Foundation (NSF) is gratefully acknowledged. This work is sponsored in part by the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement number DAAH04-952-0003/ contract number DAAH04-95-C-0008, the content of which does not necessarily reflect the position or the policy of the government, and no official endorsements hould be inferred.",

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PY - 1998/9/21

Y1 - 1998/9/21

N2 - Boundaries and boundary conditions are an aspect of the numerical solution of partial differential equations where meshless methods have had to surmount many initial difficulties due to the lack of a finite-element-like Kronecker delta condition. Furthermore, it is frequently desirable, especially in fluid mechanics, to impose general, nonlinear boundary and interface constraints. This paper describes a computationally efficient algorithm based on d'Alembert's principle that can be used for general constraints both in meshless methods and finite elements. First, a method of partitioning meshless shape functions suitable for imposing linear boundary conditions is developed. Subsequently, an analogous method is developed for nonlinear constraints. Special attention is given to imposing general boundary and fluid - structure interface conditions on the Navier-Stokes equations in terms of conservative variables. Numerical results using d'Alembert's principle with the Reproducing Kernel Particle Method (RKPM), including viscous, supersonic flow past a NACA 7012 airfoil, are shown.

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Implementation of boundary conditions for meshless methods

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