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MPHASE

The MPHASE keyword defines options for the MPHASE supercritical CO${}_2$subsurface flow mode. For more details and governing equations see the Theory Guide.

SIMULATION Options

TIMESTEPPER Options

NEWTON_SOLVER Options

Examples

SIMULATION Options

(under SUBSURFACE_FLOW in SIMULATION PROCESS_MODELS block)

TIMESTEPPER Options

Basic Settings

CFL_GOVERNOR

Specifies a maximum CFL (Courant–Friedrichs–Lewy) number that governs time step size. Subsequent time steps are calculated as a function of the maximum flow velocity and grid discretization such that the CFL is not exceeded.

CONCENTRATION_CHANGE_GOVERNOR

Specifies a maximum absolute change in concentration [mole fraction] that governs time step size. Subsequent time steps are calculated such that the governing concentration change is not exceeded.

PRESSURE_CHANGE_GOVERNOR

Specifies a maximum absolute change in pressure [Pa] that governs time step size. Subsequent time steps are calculated such that the governing pressure change is not exceeded.

SATURATION_CHANGE_GOVERNOR

Specifies a maximum absolute change in saturation [-] that governs time step size. Subsequent time steps are calculated such that the governing saturation change is not exceeded.

TEMPERATURE_CHANGE_GOVERNOR

Specifies a maximum absolute change in temperature [C] that governs time step size. Subsequent time steps are calculated such that the governing temperature change is not exceeded.

NEWTON_SOLVER Options

Basic Settings

ANALYTICAL_JACOBIAN

Calculate derivatives in Jacobian analytically.

ATOL <float>

Declare convergence when the 2-norm of residual is less than ATOL $(\Vert f(x_n)\Vert <\text{ATOL})$. (default: ${10}^{-50}$).

CONVERGENCE_INFO

Opens a block for toggling ON/OFF convergence information in screen output (default: YES to all). See example below.

• 2R, FNORM, 2NORMR - 2-norm of residual

• 2X, XNORM, 2NORMX - 2-norm of solution

• 2U, UNORM, 2NORMU - 2-norm of update

• IR, INORMR - inifinity norm of residual

• IU, INORMU - inifinity norm of update

DTOL <float>

Declare divergence (cut the time step) when the 2-norm of the residual is greater than DTOL times the 2-norm of the initial residual $(\frac{\Vert f(x_n)\Vert }{\Vert f(x_0)\Vert }>\text{DTOL})$. (default: ${10}^4$).

ITOL <float>

Declare convergence when the infinity norm of residual is less than ITOL $(\Vert f(x_n){\Vert }_{inf}<\text{ITOL})$. (default: not used).

MAXIMUM_NUMBER_OF_ITERATIONS <int>

Maximum number of Newton iterations before reporting failed convergence.

NO_PRINT_CONVERGENCE

Toggle off printing of convergence information.

NTRDC_OPTIONS or NTR_OPTIONS

Opens a block for trust-region options and parameters (SNES_TYPE NTRDC or SNES_TYPE NTR required)

• TR_TOL - trust-region tolerance (default: ${1.0}^{-12}$)

• ETA1 - trust-region parameter $0.0\le {\eta }_1\le {\eta }_2$, $\rho \ge {\eta }_1$ breaks out of the inner iteration (default: ${\eta }_1=0.001$)

• ETA2 - trust-region parameter $0.0\le {\eta }_1\le {\eta }_2$, $\rho \ge {\eta }_2$ shrinks the trust-region (default: ${\eta }_2=0.25$)

• ETA3 - trust-region parameter ${\eta }_3>{\eta }_2$, $\rho \ge {\eta }_3$ expands the trust-region (default: ${\eta }_3=0.75$)

• T1 - trust-region parameter, shrinking factor of trust-region (default: 0.25)

• T2 - trust-region parameter, initial size of trust-region, ${\mathrm{\Delta }}_0\ast \Vert x{\Vert }_2$ (default: 0.1)

• DELTA_M - trust-region parameter, max size of trust-region, ${\mathrm{\Delta }}_M\ast \Vert x{\Vert }_2$ (default: 0.5)

• DELTA_0 - trust-region parameter, initial size of trust-region, ${\mathrm{\Delta }}_0\ast \Vert x{\Vert }_2$ (default: 0.1)

• AUTO_SCALE - TRUE enables solution update scaling meaning all types of unknowns are equally treated when evaluating solution update (recommended for WIPP-FLOW, TH); FALSE disables solution update scaling meaning that solution update evaluation will focus more on pressure than other unknowns (recommended for GENERAL, HYDRATE).

• AUTO_SCALE_MAX - used with AUTO_SCALE, caps the maximum auto-scaling factor

NUMERICAL_JACOBIAN

Calculate derivatives in Jacobian numerically.

PRINT_LINEAR_ITERATIONS

Prints the number of linear iterations for each Newton iteration to the screen.

RTOL <float>

Declare convergence when the 2-norm of the residual is less than RTOL times the 2-norm of the initial residual $(\frac{\Vert f(x_n)\Vert }{\Vert f(x_0)\Vert }<\text{RTOL})$. (default: ${10}^{-8}$).

SNES_TYPE <string>

The default is LINE_SEARCH (Basic, see PETSc documenetation) from PETSc which is Newton-Raphson nonlinear solver. NTRDC is the Newton Trust-Region Dogleg-Cauchy nonlinear solver, and NTR is the Newton Trust-Region nonlinear solver. The difference between NTRDC and NTR is that NTRDC adds steepest-descent solution update to the Newton solution iff it optimizes better than Newton solution alone within the trust-region. NTR only applies Newton solution update and it is truncated by the trust-region. NTRDC MAY perform better with LESS phase state change simulations for GENERAL MODE.

STOL <float>

Declare convergence when the 2-norm of the update divided by the 2-norm of the solution is less than STOL $(\frac{\Vert x_n-x_{n-1}\Vert }{\Vert x_{n-1}\Vert }<\text{STOL})$. (default: ${10}^{-8}$).

VERBOSE_LOGGING

Prints additional convergence information to screen.

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Expert Settings

MATRIX_TYPE <string>

Format of main solver matrix. PETSc Mat (i.e. AIJ, BAIJ, or HYPRESTRUCT).

MAXF <int>

Maximum number of function evaluations before reporting failed convergence.

MAX_NORM <float>

Declare divergence (cut the time step) when the infinity norm of the residual is greater than MAX_NORM $(\Vert f(x_n){\Vert }_{inf}>\text{MAX\_NORM})$. (default: ${10}^{20}$).

MINIMUM_NUMBER_OF_ITERATIONS <int>

Newton solver convergence requires at least MINIMUM_NUMBER_OF_ITERATIONS.

NO_FORCE_ITERATION

Toggle off the forcing of at least 1 linear iteration. The default is to force at least 1 linear iteration. In a quasi-stationary state, the initial residual may be sufficiently small for convergence, but often it is better to force at least one iteration.

NO_INFINITY_NORM

Toggle off calculation of infinity norm on residual and update vectors. The default is to calculate the infinity norm.

PRECONDITIONER_MATRIX_TYPE <string >

Format of preconditioning matrix. PETSc Mat (i.e. AIJ, BAIJ, or HYPRESTRUCT). Default is same as solver.

PRINT_DETAILED_CONVERGENCE

Toggle on printing of detailed convergence information.

Examples

SIMULATION
  SIMULATION_TYPE SUBSURFACE
  PROCESS_MODELS
    SUBSURFACE_FLOW flow
      MODE MPHASE
    /
  /
END
...
SUBSURFACE
  NUMERICAL_METHODS FLOW
    TIMESTEPPER
      TS_ACCELERATION 8
      PRESSURE_CHANGE_GOVERNOR 5.e4
      TEMPERATURE_CHANGE_GOVERNOR 5.d0
      CONCENTRATION_CHANGE_GOVERNOR 1.e-2
      SATURATION_CHANGE_GOVERNOR 0.025
    /
    NEWTON_SOLVER
      ATOL 1.d-12
      RTOL 1.d-12
      STOL 1.d-30
      DTOL 1.d15
      ITOL 1.d-8
      MAXIMUM_NUMBER_OF_ITERATIONS 25
      MAXF 100
    /
  /
  ...