Implementasi Metode Elemen Hingga Galerkin dalam Model Difusi-Adveksi 2D Untuk Penyebaran Inokulum pada Pohon Gaharu

Abstract

Agarwood is a high value resin widely used in the beauty, perfume, and pharmaceutical industries. However, the availability of high-quality agarwood remains limited, partly due to the uneven distribution of inoculum during the artificial inoculation process. This study analyzes this phenomenon from a mathematical perspective, as distribution imbalances directly impact the quality and quantity of the resin. Therefore, an approach is needed that is not only descriptive but also capable of predicting inoculum dispersion patterns in a measurable way. This study aims to develop a two-dimensional diffusion-advection model and implement the finite element method using the Galerkin approach as a numerical solution technique. The model is formulated as a non-stationary partial differential equation, then converted to a weak form and discretized using triangular elements. Calculations are performed through a combination of manual analysis and numerical simulation using MATLAB, with variations in the number and position of injection sources. Simulation results show that mesh density affects accuracy, where a fine mesh produces a smoother and more stable distribution. Furthermore, the number and orientation of injection sources play a significant role in the uniformity of the distribution. The two- and four-source configurations still produce a concentrated distribution, while the six and eight source configurations show a more even distribution. Although the eight-source configuration yields the most homogeneous results, the six-source configuration was selected as the optimal solution because it is more efficient and still produces a sufficiently good distribution.