382 IGPM382.pdf        January 2014
TITLE Flux Splitting: A Notion on Stability
AUTHORS Sebastian Noelle, Jochen Schütz
ABSTRACT In the context of low Mach number flows, successful methods are Asymptotic Preserving and IMEX schemes. Both schemes for hyperbolic equations rely on a splitting of the convective flux into stiff and nonstiff parts. This choice is not arbitrary and has an influence on both the stability and the accuracy of the resulting methods. In this work, we consider a first-order IMEX scheme based on different splittings. Using the modified equation approach, we can show that a new class of splittings based on characteristic decomposition, also introduced in this work, gives rise to a stable method with a time step independent of the small quantity ε, whereas a splitting taken from literature can be identified to be stable only for small values of the CFL number.
KEYWORDS IMEX finite volume, asymptotic preserving, flux splitting, modified equation, stability analysis
DOI 10.1007/s10915-014-9942-x
PUBLICATION Journal of Scientific Computing
Volume 63, 1986 - 2015