Operator-Split Lagrangian-Eulerian Time Integration
H.N. Najm, R.B. Milne, J. Ray, K.D. Devine and S.N. Kempka
Submitted to J. Computational Physics, 2000.

The Particle Strength Exchange (PSE) scheme is useful for modeling diffusion of vorticity in a purely Lagrangian numerical construction. This is done in a fully-coupled non-split implementation of diffusion and convection. Unfortunately, there is no similarly general Lagrangian scheme for modeling the arbitrary circulation source terms, such as those due to baroclinic vorticity generation in a reacting flow environment. We present and analyze both non-split and split hybrid Lagrangian-Eulerian formulations that allow the modeling of baroclinic vorticity generation. We find that the non-split implementation, even though fully coupled, does not achieve second-order time accuracy in the context of a second-order Runge-Kutta construction. On the other hand, the symmetric operator-split formulation does achieve second-order convergence, and is clearly superior in this context. This formulation is being presently used in the context of hybrid Lagrangian-Eulerian computations of reacting flow.