Create two phase solver for saturated soil with explicit method

Summary

Create ExplicitTwoPhase solver with fully saturated condition to carry out the hydraulic coupled computation. A one-point two phase method based on volume fractions is used to represent the solid phase and water phase on the same particle representively.

Motivation

Use it to compute the hydraulic coupled problem. It's the foundation of following implementation of SemiImplicitTwophase solver and even ThreePhase solvers.

Design Detail

1. Node base design
   The computation is mainly based on solving the momentum balance equations of mixture and water phase on nodes. (There are three different sections to represent the domain, solid phase, water phase and mixture). As solving two of them is enough to obtain the results, we solve the mixture first and then the water phase. Therefore, in the node class, all variables, like velocity, are designed and stored as 0 for mixture and 1 for water phase.

2. Particle class design
   Different with the node class, all variables in the particle class are designed and stored as 0 for solid and 1 for water phase, which is convenient to represent the effective stress and other variables. A "TwoPhaseParticle" namespace is created to include the functions and variables used.

2.1. New variables for two phase particle
Scalar type
porosity, liquid_material_id, liquid_mass, liquid_mass_density,
pore_pressure, pore_pressure_constraint
Vector type
liquid_velocity, liquid_strain, permeability
Map type
liquid_velocity_constraints
Other type
liquid_material
2.2. Current function need to be modified
initialise_particle, hdf5, compute_mass
2.3. New functions for two phase
compute_pore_pressure, update_permeability

3. Solver class design
   A mpm-explicit-twophase is created in the solver class. The main loop is quite similar with the mpm-explicit solver, but the mapping functions are used for each phase separately. compute_pore_pressure is an important additional function in the TwoPhase solver based on the Darcy law. The position update is based on the solid phase velocity.

4. Based on porous medium theory:
   The volume_fractions_ is defined in the particle class based on the porous medium theory and is used to compute the variables in each phase.

5. Fully saturated condition:
   The sum of volume_fractions_ should be equal to 1 and updated in each step.

6. An option is considered for the choice of formulation type (u-p,u-v-p,u-w-p)

Drawbacks

1. The critical size of time interval is influenced by the water phase,
2. The permeability can not be too small to form large fluctuation.

Rationale and Alternatives

Create semi-implicit solver based on incompressible flow hypothesis in the future.

Prior Art

One can refer to the following papers:
[1] Kafaji, Issam KJ al. Formulation of a dynamic material point method (MPM) for geomechanical problems. 2013.
[2] Jassim, Issam, Dieter Stolle, and Pieter Vermeer. "Two‐phase dynamic analysis by material point method." International journal for numerical and analytical methods in geomechanics 37.15 (2013): 2502-2522.
[3] Zabala F, Alonso E E. Progressive failure of Aznalcóllar dam using the material point method[J]. Géotechnique, 2011, 61(9): 795-808.