Issues in Eulerian-Lagrangian Simulation of Complex Multiphase Flow and Transport

A complex multiphase multicomponent flow, such as a compositional oil reservoir or a multicontaminant aquifer system, is challenging to simulate numerically. Some of the complications, such as strong nonlinear coupling and phase changes, are inherent in the physics. Others, including CFL time-step restrictions and tradeoffs between oscillations and numerical diffusion, are computational artifacts. Eulerian-Lagrangian methods seek to eliminate the artifacts via an operator splitting, in which mass advection in all phases constitutes one fractional step of a Newton iteration of a time step. This can be viewed physically in a tantalizingly simple way: take each phase velocity field as known in the advection step, advect finite volumes (or particles) of mass in each phase, then perform other fractional steps, and iterate. It turns out that this particle-oriented view of multiphase flow is expressed by a natural dual adjoint formulation, which is arguably closer to the physics and whose properties are more tractable than those of the primal wave-oriented system. Practical realization of this program is not as simple. The speaker will discuss technical issues, such as Lagrangian tracking and mass and volume conservation, and will present analytical and numerical examples.

Thomas Russell, National Science Foundation

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