Flux Splitting: A Notion on Stability

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.