An Approximation of a Linear Advection Equation using the Meshfree Method

Abstract

In this paper, a mesh-free method called “Smoothed Particle Hydrodynamics (SPH)” is applied to the linear advection equation. The cubic spline weight function is used to determine the advection field at the nodes from particles in the support domain. After the nodes have been defined, the derivative of the function is approximated from the derivative of the weight function. This is equivalent to finding the changes in distance between nodes. Results obtained from the SPH method are compared with the corresponding exact solutions. Effects of boundary condition are also investigated.

Keywords: Smoothed Particle Hydrodynamics, Advection equation

E-mail: dusadee.suk@kmutt.ac.th

How to Cite

Citation Format

Koomsubsiri, A. ., Sukawat*, D. ., & Tangmanee, S. . (2018). An Approximation of a Linear Advection Equation using the Meshfree Method. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 111-117.

References

[1] Liu, G.R., 2003. Meshfree Methods Moving beyond the Finite Element Method, Boca Raton,CRC Press.
[2] Li, S. and Liu, W.K., 2004. Meshfree Particle Methods, New York, Springer.
[3] Liu, M.B., Liu, G.R. and Lam, K.Y., 2002. Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of Computational and Applied Mathematics, 263-284.
[4] James, R.H. and Thomas, R.H., 2004. An Introduction to Dynamic Meteorology, 4th ed.,USA, Elsevier Inc.
[5] Smith, G.D., 1985. Numerical Solution of Partial Differential Equations, 3rd ed., United States, Clarendon Press.

Author Information

Amorn Koomsubsiri

Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

Dusadee Sukawat*

Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

Suwon Tangmanee

Centre of Excellence in Mathmatics (CEM), Faculty of Science, Mahidol University, Bangkok, Thailand

About this Article

Journal

Vol. 12 No. 2 (2012)

Type of Manuscript

Original Research Article

Keywords

Smoothed Particle Hydrodynamics, Advection equation

Published

30 March 2018

An Approximation of a Linear Advection Equation Using the Meshfree Method

Abstract

How to Cite

References

Author Information

Amorn Koomsubsiri

Dusadee Sukawat*

Suwon Tangmanee

About this Article

Journal

Type of Manuscript

Keywords

Published

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