  Mixtures of fluids and granular sediments play an important role in many
industrial, geotechnical, and aerospace engineering problems, from waste
management and transportation (liquid--sediment mixtures) to dust kick-up below
helicopter rotors (gas--sediment mixtures). These mixed flows often involve
bulk motion of hundreds of billions of individual sediment particles and can
contain both highly turbulent regions and static, non-flowing regions. This
breadth of phenomena necessitates the use of continuum simulation methods, such
as the material point method (MPM), which can accurately capture these large
deformations while also tracking the Lagrangian features of the flow (e.g.\ the
granular surface, elastic stress, etc.).
  Recent works using two-phase MPM frameworks to simulate these mixtures have
shown substantial promise; however, these approaches are hindered by the
numerical limitations of MPM when simulating pure fluids. In addition to the
well-known particle ringing instability and difficulty defining inflow/outflow
boundary conditions, MPM has a tendency to accumulate quadrature errors as
materials deform, increasing the rate of overall error growth as simulations
progress. In this work, we present an improved, two-phase continuum simulation
framework that uses the finite volume method (FVM) to solve the fluid phase
equations of motion and MPM to solve the solid phase equations of motion,
substantially reducing the effect of these errors and providing better accuracy
and stability for long-duration simulations of these mixtures.
