An Approximation of a Linear Advection Equation using the Meshfree Method
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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
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References
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