Some Practical Issues in the Implementation of Meshfree Methods with reference to the Method of Finite Spheres

2009 ◽  
Author(s):  
S. De
Keyword(s):  
Meshfree Methods ◽  
Finite Spheres

Numerical integration of the Galerkin weak form in meshfree methods

1999 ◽  
Vol 23 (3) ◽  
pp. 219-230 ◽  
Author(s):  
John Dolbow ◽  
Ted Belytschko
Keyword(s):  
Numerical Integration ◽  
Weak Form ◽  
Meshfree Methods

scholarly journals A Lagrangian Approach for Computational Acoustics with Meshfree Method

2017 ◽  
Author(s):  
Yong Ou Zhang ◽  
Stefan G. Llewellyn Smith ◽  
Tao Zhang ◽  
Tian Yun Li
Keyword(s):  
Sound Propagation ◽  
Fluid Dynamic ◽  
Taylor Series Expansion ◽  
Meshfree Method ◽  
Lagrangian Approach ◽  
Meshfree Methods ◽  
Combustion Noise ◽  
Smoothed Particle ◽  
The Time Domain ◽  
Perturbation Equations

Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

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