Acceso usuarios
Geovanne Silva Faria, Andreia Aoyagui Nascimento, Felipe Pamplona Mariano
The Burgers equation is a mathematical model frequently used in Computational Fluid Dynamics. It is often employed to test and calibrate numerical methods, as it is one of the few nonlinear transport equations with an exact analytical solution. In this paper, numerical solutions are obtained using the Finite Difference Method (FDM) and the Fourier Pseudospectral Method (FPSM) for spatial discretization, combined with the Euler Method and the Fourth-Order Runge-Kutta Method (FRKM) for time discretization. The results are compared with the exact analytical solution in terms of accuracy, convergence rate, and computational cost. The findings indicate that the combination of the FDM and Euler Method achieves excellent computational efficiency when compared to the other approaches. Meanwhile, the combination of FPSM and FRKM demonstrates superior accuracy (achieving round-off errors) and a high order of convergence (spectral convergence order). Thus, combining methods with similar convergence rates and accuracy is the optimal strategy for obtaining efficient numerical solutions of partial differential equations (PDEs).
