DEVELOPMENT OF THE FINITE DIFFERENCE METHOD FOR VORTICITY FLOW SIMULATION USING THE FOURTH-ORDER RUNGE-KUTTA METHOD Aldiansyah Anugrah Ramadhan (a*), Ikha Magdalena (a), Hakim Luthfi Malasan (a), Acep Purqon (a)
(a) Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132, Indonesia
*aldiansyahaldi621[at]gmail.com
Abstract
The finite difference method is a numerical method to solve partial differential equations. The Forward Time Centered Space (FTCS) is an explicit finite difference method employed to solve parabolic partial differential equations. However, the FTCS scheme has a strict stability condition, requiring a very small time step. To address this limitation, this study integrates the centered difference scheme with fourth-order Runge-Kutta method (RK4), yielding the RK4-CS scheme. The RK4-CS scheme is applied to simulate vorticity flow in a lid-driven cavity system. Validation is conducted by comparing the flow structures and computing error values using the Mean Absolute Percentage Error (MAPE) with the results from prior studies. The simulation results show that the vorticity flow structures obtained from the RK4-CS scheme are consistent with the results of prior studies. The MAPE values obtained from the RK4-CS scheme with time steps exceeding the stability limit of the FTCS scheme under the laminar regime is 2.3013%.
