TY - JOUR
T1 - Implementation of boundary conditions for meshless methods
AU - Günther, Frank C.
AU - Liu, Wing Kam
N1 - 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.
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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0032154328&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032154328&partnerID=8YFLogxK
U2 - 10.1016/S0045-7825(98)00014-0
DO - 10.1016/S0045-7825(98)00014-0
M3 - Article
AN - SCOPUS:0032154328
SN - 0045-7825
VL - 163
SP - 205
EP - 230
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 1-4
ER -