Numerical Experiments for Time Integration of 2D Burgers’ Equations

Resumo

Numerical solution of partial differential equations requires the choice of a time integration method capable of simulating the evolution of a problem. While traditional methods are usually categorized into explicit and implicit, each with their own sets of advantages and disadvantages, a more recent approach is the combination of both types into the so called IMEX schemes. These were designed to solve equations containing fast and slow time-scales in such a way that the slow terms can be solved explicitly, while the slow terms are solved implicitly, mitigating the disadvantages of each individual scheme. In this work, the finite difference approach is used to solve a two-dimensional, viscous Burgers’ system in a series of numerical experiments using each of the aforementioned time integration schemes