IMEX Schemes for Time Integration of Burgers' Equation

Antonio Maurício Zarzur¹; Haroldo Fraga de Campos Velho¹; Stephan Stephany¹; Saulo Ribeiro de Freitas²

¹ INPE; ² NASA

doi:10.20906/CPS/CILAMCE2017-0786

Resumo

Standard numerical methods for time-integration are usually categorized into explicit and implicit, each with their own sets of advantages and disadvantages. A more recent formulation combines 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 fast terms are solved implicitly, mitigating the disadvantages of each individual scheme. Adams-Bashforth (explicit) and Crank-Nicolson (implicit) are employed in the IMEX scheme for the Burger's equation. A comparison is done with IMEX approach and fully explicit and implicit formulations.

Palavras-chave: Computational fluid dynamics; Burger's equation; IMEX approach