Dual Reciprocity Boundary Element Method untuk Menyelesaikan Masalah Infiltrasi Stasioner pada Saluran Datar Periodik

M. Megasari(1*),

(1) Institut Agama Islam Negeri Palopo
(*) Corresponding Author




DOI: https://doi.org/10.35580/jmathcos.v4i1.20447

Abstract


Abstrak. Penelitian ini membahas tentang penyelesaian masalah infiltrasi stasioner dari saluran datar dengan Dual Reciprocity Boundary Element Method (DRBEM). Persamaan pembangun untuk masalah ini adalah persamaan Richard. Menggunakan transformasi Kirchhoff dan relasi eksponensial konduktifitas hidrolik, persamaan Richard ditransformasi ke dalam persamaan infiltrasi stasioner dalam Matric Flux Potential (MFP). Persamaan infiltrasi dalam MFP selanjutnya diubah ke dalam persamaan Helmholtz termodifikasi. Model matematika infiltrasi stasioner pada saluran datar berbentuk Masalah Syarat batas Helmholtz termodifikasi Solusi numerik diperoleh dengan menyelesaikan persamaan Helmholtz termodifikasi menggunakan Dual Reciprocity Boundary Element Method (DRBEM) dengan pengambilan jumlah titik kolokasi eksterior dan interior yang bervariasi. Lebih lanjut, solusi numerik dan solusi analitik dibandingkan..

Kata Kunci: Infiltrasi, saluran datar, persamaan helmholtz termodifikasi, DRBEM.

Abstract. This research discusses about the problem solving of steady infiltration problem from flat channel with Dual Reciprocity Boundary Element Method (DRBEM). The governing equation for this problem is Richard’s equation. Using Kirchhoff transformation and exponential hydraulic conductivity relation, Richard’s equation is transformed into steady infiltration equation in the form of MFP. Infiltration equation in the form of MFP is then transformed to modified Helmholtz equation. A mathematical model of steady infiltration from flat channel in the form of boundary condition problem of modified Helmholtz EQUATION. Numerical solution is obtained by solving modified Helmholtz equation by using Dual Reciprocity Boundary Element Method (DRBEM) with various number of exterior and interior collocation points. Moreover, numerical and analytic solution are then compared.

Keywords: infiltration, flat channel, modified Helmholtz equation, DRBEM


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References


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