# RESOLUTION OF THE INFILTRATION PROBLEM FROM PERIODIC FLAT CHANNEL USING DUAL RECIPROCITY BOUNDARY ELEMENT METHOD WITH A RADIAL BASE FUNCTION

• Faustianus Luan Universitas Timor
• Elinora Naikteas Bano Universitas Timor
Keywords: Keywords: Infiltration, modified Helmholtz equation, FBR, DRBEM.

### Abstract

This research discusses the numerical solution of the infiltration problem of the periodic flat channel and is solved using the Dual Reciprocity Boundary Element Method (DRBEM)  numerical method with polynomial radial basis functions. DRBEM is a development of the Boundary Element Method, used for PDP solutions in the fields of mathematical physics and engineering. DRBEM has an important role in obtaining a solution to the Helmholtz equation by describing the reciprocal relation between the fundamental solution of the Laplace equation and the solution to be sought. Furthermore, the term containing the double integral in the calculation is approximated by the radial basis function, in order to obtain an equation containing only the boundary integral. The objective of the obtained numerical solution is then compared with the analytical solution obtained by Batu, in order to obtain an accurate solution of the polynomial radial base function for solving the infiltration problem. The mathematical models used in the infiltration problem are the Richards equations, Kirchoff transformation and the dimensionless variables for obtaining the modified Helmholtz equation. The results of the calculation of the numerical solution have shown that the DRBEM with the radial polynomial base function for the number of boundary elements resulting from the discretization and the number of interior collocation points at (N = 200, L = 400) and (N = 225, L = 400) obtained the approximate value ( error) from the six points in the region, indicating that the greater the value of N, the smaller the error. So that for FBR, and  the one with the smallest error is , it means that it is close to the FBR used by Batu, is .. Thus, it is concluded that the more discrete line segments result in the region boundary, the numerical solution will approximate the analytical solution. Keywords: Infiltration, modified Helmholtz equation, FBR, DRBEM.

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Published
2021-08-04
How to Cite
Luan, F., & Bano, E. (2021). RESOLUTION OF THE INFILTRATION PROBLEM FROM PERIODIC FLAT CHANNEL USING DUAL RECIPROCITY BOUNDARY ELEMENT METHOD WITH A RADIAL BASE FUNCTION. Jurnal Saintek Lahan Kering, 4(1), 1-4. https://doi.org/https://doi.org/10.32938/slk.v4i1.1375
Section
Original research article