P2Pflow:  a Parallel two-Phase flow solver

A parallel finite element solver for incompressible two-phase flow problems on 3D unstructured mesh. The solver is scalable on supercomputers such as Tianhe2 and Shaheen2 with 10,000+ cores.

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Module 1.  A semi-implicit linear solver for the phase-field model with Cahn-Hilliard-Navier-Stokes equations, used for the simulation of liquid-gas-solid interaction, i.e. the wetting phenomenon. Ref.

The study of the wetting phenomenon is of critical importance in many industrial applications such as coating, ink-jet printing, and microfluidics. Interesting wetting behavior occurs when micrometric spatial dimension comes into play, as a result roughness-enhanced wetting has become the subject of extensive investigation.

Features of Module 1:

• • A phase-field model consisting of the coupled Cahn–Hilliard-Navier–Stokes equations with a generalized Navier boundary condition (GNBC).
  • A semi-implicit time discretization method is used to decouple the system into three subsystems for the phase function, the velocity, and the pressure, respectively.
  • A linearly convex-splitting method is used to handle the high order derivatives and high nonlinearity in the Cahn–Hilliard equation.
  • A finite element method on unstructured 3D meshes for problems in complex geometries.
  • A highly parallel solution strategy using different solvers for different components of the discretization.                               

Partition of unstructured mesh into subdomainsSpreading of a droplet over a rough surface

Spreading of a droplet over a substrate with micropillars

Module 2.   A fully implicit nonlinear solver for the two-phase flow governed by Darcy law in porous media, used for oil reservoir simulation. Ref.

Simulation of flows in subsurface porous media plays an important role in the performance of petroleum reservoir and the assessment of groundwater contamination. The extended Darcy’s law accounting for the properties of both fluid and media is often used to address multiphase flow, and the complexity of this model lies in the interaction of various modeling features, including gravity, capillary pressure effects, heterogeneity of the absolute permeability, and relative permeability functions. Extra difficulties are induced by complex geometry, faults, channels and deviated wells, etc. In general, useful results for a large-scale geological model with complex heterogeneity are obtained by using numerical methods on meshes with millions or even billions of points, accurate discretization schemes, and efficient parallel solution algorithms.

Features of Module 2:

• • A fully implicit discontinuous Galerkin discretization for the extended Darcy’s law on 3D unstructured meshes.
  • An inexact Newton-Krylov algorithm with analytic Jacobian is used to solve the nonlinear systems.
  • A hybrid two-level version of the additive Schwarz preconditioner consisting of a nested coarse space is used to improve the robustness and scalability.
  • Nonlinear preconditioning is applied to balance the nonlinearities of the overall system so that fast convergence can be realized.

Simulation of two-phase flows in oil reservoir (Case SPE10)

The framework of P2Pflow