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COMBINED EXPLICIT AND IMPLICIT METHODS FOR TIME INTEGRATION IN PARTIAL DIFFERENTIAL EQUATIONS

Antonio M. Zarzur
Instituto Nacional de Pesquisas Espaciais, Sao Jose dos Campos, SP, 12227-010, Brazil

Haroldo F. de Campos Velho
Institute Nacional de Pesquisas Espaciais (INPE), Caixa Postal 515, 12201-970 São José dos Campos - SP, Brazil

Saulo R. Freitas
NASA Goddard Space Flight Center, Greenbelt, MD, 20771, USA

Stephan Stephany
Instituto Nacional de Pesquisas Espaciais, Sao Jose dos Campos, SP, 12227-010, Brazil

DOI: 10.1615/TFEC2018.cfd.021966
pages 151-158


KEY WORDS: Computational fluid dynamics, IMEX method, Burger's equations

Abstract

Numerical methods for the solution of partial differential equations are broadly categorized as either implicit or explicit. A more recent approach, denominated IMEX, takes advantage of both strategies to form a combined scheme that excels in the solution of problems containing both fast and slow time scales. In this work, a family of multistep IMEX schemes based on Adams methods is used to solve the two-dimensional viscous Burgers' equation, which is one of the fundamental equations in fluid dynamics. Two numerical experiments are proposed, where the exact solution is used to verify the results, and the accuracy of the proposed methods is compared to a fully explicit and a fully implicit implementation.

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