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A corrective smoothed particle method for boundary value problems in heat conduction. (English) Zbl 0941.65104

A combination of the kernel estimate with the Taylor series expansion is proposed to develop a corrective smoothed particle method. This algorithm resolves the general problem of particle deficiency at boundaries, which is a shortcoming in standard smoothed particle hydrodynamics. In addition the method’s ability to model derivatives of any order could make it applicable for any time-dependent boundary value problems.
An example of the applications studied in this paper is unsteady heat conduction, which is governed by second-order derivatives. Numerical results demonstrate that besides the capability of directly imposing boundary conditions, the present method enhances the solution accuracy not only near or on the boundary but also inside the domain.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65C35 Stochastic particle methods
35K05 Heat equation

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References:

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