8.3.3. Numerical Parameters

This section contains keywords for defining numerical parameters. Keywords related to solving the governing equations (e.g., LEQ_IT, DISCRETIZE, UR_FAC, etc.) are dimensioned for the ten types of equations:

Index

Equation Type

1

Gas Pressure

2

Solids Volume Fraction

3

Gas and Solids U Momentum Equation

4

Gas and Solids V Momentum Equation

5

Gas and Solids W Momentum Equation

6

Gas and Solids Energy Equations (Temperature)

7

Gas and Solids Species Mass Fractions

8

Granular Temperature

9

User-Defined Scalar and K-Epsilon Equation

10

DES Diffusion Equation

For example, LEQ_IT(3) = 10, specifies to use 10 iterations within the linear equation solver for the U Momentum Equations (of type 3).

8.3.3.1. MAX_NIT

Data Type: INTEGER

Maximum number of iterations [500].

8.3.3.2. NORM_G

Data Type: DOUBLE PRECISION

Factor to normalize the gas continuity equation residual. The residual from the first iteration is used if NORM_G is left undefined. NORM_G=0 invokes a normalization method based on the dominant term in the continuity equation. This setting may speed up calculations, especially near a steady state and for incompressible fluids. But, the number of iterations for the gas phase pressure, LEQ_IT(1), should be increased to ensure mass balance.

8.3.3.3. NORM_S

Data Type: DOUBLE PRECISION

Factor to normalize the solids continuity equation residual. The residual from the first iteration is used if NORM_S is left undefined. NORM_S = 0 invokes a normalization method based on the dominant term in the continuity equation. This setting may speed up calculations, especially near a steady state and incompressible fluids. But, the number of iterations for the solids volume fraction, LEQ_IT(2), should be increased to ensure mass balance.

8.3.3.4. TOL_RESID

Data Type: DOUBLE PRECISION

Maximum residual at convergence (Continuity + Momentum) [1.0d-3].

8.3.3.5. TOL_RESID_T

Data Type: DOUBLE PRECISION

Maximum residual at convergence (Energy) [1.0d-4].

8.3.3.6. TOL_RESID_X

Data Type: DOUBLE PRECISION

Maximum residual at convergence (Species Balance) [1.0d-4].

8.3.3.7. TOL_RESID_TH

Data Type: DOUBLE PRECISION

Maximum residual at convergence (Granular Energy) [1.0d-4].

8.3.3.8. TOL_RESID_SCALAR

Data Type: DOUBLE PRECISION

Maximum residual at convergence (Scalar Equations) [1.0d-4].

8.3.3.9. TOL_RESID_K_EPSILON

Data Type: DOUBLE PRECISION

Maximum residual at convergence (K_Epsilon Model) [1.0d-4].

8.3.3.10. TOL_DIVERGE

Data Type: DOUBLE PRECISION

Minimum residual for declaring divergence [1.0d+4]. This parameter is useful for incompressible fluid simulations because velocity residuals can take large values for the second iteration (e.g., 1e+8) before dropping down to smaller values for the third iteration.

8.3.3.11. DETECT_STALL

Data Type: LOGICAL

Reduce the time step if the residuals stop decreasing. Disabling this feature may help overcome initial non-convergence.

Table 8.17 Valid Values

Name

Default?

Description

.FALSE.

Continue iterating if residuals stall.

.TRUE.

Reduce time step if residuals stall.

8.3.3.12. LEQ_METHOD(EQUATION ID NUMBER)

Data Type: INTEGER

  • \(1 \le Equation ID Number \le 10\)

LEQ Solver selection. BiCGSTAB is the default method for all equation types.

Table 8.18 Valid Values

Name

Default?

Description

1

SOR - Successive over-relaxation

2

BiCGSTAB - Biconjugate gradient stabilized.

3

GMRES - Generalized minimal residual method

5

CG - Conjugate gradient

8.3.3.13. LEQ_TOL(EQUATION ID NUMBER)

Data Type: DOUBLE PRECISION

  • \(1 \le Equation ID Number \le 10\)

Linear Equation tolerance [1.0d-4].

8.3.3.14. LEQ_IT(EQUATION ID NUMBER)

Data Type: INTEGER

  • \(1 \le Equation ID Number \le 10\)

Number of iterations in the linear equation solver.

Default value: - 20 iterations for equation types 1-2 - 5 iterations for equation types 3-5,10 - 15 iterations for equation types 6-9

8.3.3.15. LEQ_SWEEP(EQUATION ID NUMBER)

Data Type: CHARACTER

  • \(1 \le Equation ID Number \le 10\)

Linear equation sweep direction. This applies when using GMRES or when using the LINE preconditioner with BiCGSTAB or CG methods. ‘RSRS’ is the default for all equation types.

Table 8.19 Valid Values

Name

Default?

Description

RSRS

(Red/Black Sweep, Send Receive) repeated twice

ISIS

(Sweep in I, Send Receive) repeated twice

JSJS

(Sweep in J, Send Receive) repeated twice

KSKS

(Sweep in K, Send Receive) repeated twice

ASAS

(All Sweep, Send Receive) repeated twice

8.3.3.16. LEQ_PC(EQUATION ID NUMBER)

Data Type: CHARACTER

  • \(1 \le Equation ID Number \le 10\)

Linear preconditioner used by the BiCGSTAB and CG LEQ solvers. ‘LINE’ is the default for all equation types.

Table 8.20 Valid Values

Name

Default?

Description

NONE

No preconditioner

LINE

Line relaxation

DIAG

Diagonal Scaling

8.3.3.17. UR_FAC(EQUATION ID NUMBER)

Data Type: DOUBLE PRECISION

  • \(1 \le Equation ID Number \le 10\)

Under relaxation factors. Default value: - 0.8 for equation types 1,9 - 0.5 for equation types 2,3,4,5,8 - 1.0 for equation types 6,7,10

8.3.3.18. UR_F_GS

Data Type: DOUBLE PRECISION

The implicitness calculation of the gas-solids drag coefficient may be underrelaxed by changing ur_f_gs, which takes values between 0 to 1.

  • 0 updates F_GS every time step

  • 1 updates F_GS every iteration

8.3.3.19. UR_KTH_SML

Data Type: DOUBLE PRECISION

Under relaxation factor for conductivity coefficient associated with other solids phases for IA Theory [1.0].

8.3.3.20. DISCRETIZE(EQUATION ID NUMBER)

Data Type: INTEGER

  • \(1 \le Equation ID Number \le 10\)

Discretization scheme used to solve equations.

Table 8.21 Valid Values

Name

Default?

Description

0

First-order upwinding.

1

First-order upwinding (using down-wind factors).

3

Smart.

2

Superbee (recommended method).

5

QUICKEST (does not work).

4

ULTRA-QUICK.

7

van Leer.

6

MUSCL.

8

minmod.

9

Central (often unstable; useful for testing).

8.3.3.21. DEF_COR

Data Type: LOGICAL

Use deferred correction method for implementing higher order discretization.

Table 8.22 Valid Values

Name

Default?

Description

.FALSE.

Use down-wind factor method (default).

.TRUE.

Use deferred correction method.

8.3.3.22. CHI_SCHEME

Data Type: LOGICAL

This scheme guarantees that the set of differenced species mass balance equations maintain the property that the sum of species mass fractions is one. This property is not guaranteed when a flux limiter is used with higher order spatial discretization schemes. Note: The chi-scheme is implemented for SMART and MUSCL discretization schemes. Darwish, M.S., Moukalled, F. (2003). Computer Methods in Applied Mech. Eng., 192(13):1711-1730.

Table 8.23 Valid Values

Name

Default?

Description

.FALSE.

Do not use the chi-scheme.

.TRUE.

Use the chi-scheme correction.

8.3.3.23. CN_ON

Data Type: LOGICAL

Temporal discretization scheme.

Table 8.24 Valid Values

Name

Default?

Description

.FALSE.

Implicit Euler based temporal discretization scheme employed (first-order accurate in time).

.TRUE.

Two-step implicit Runge-Kutta method based temporal discretization scheme employed. This method should be second- order accurate in time excluding pressure terms and restart time step which are first-order accurate. However, as of 2015, testing shows that second-order accuracy is not observed.

8.3.3.24. MAX_INLET_VEL_FAC

Data Type: DOUBLE PRECISION

The code declares divergence if the velocity anywhere in the domain exceeds a maximum value. This maximum value is automatically determined from the boundary values. The user may scale the maximum value by adjusting this scale factor [1.0d0].

8.3.3.25. DO_TRANSPOSE

Data Type: LOGICAL

Solve transpose of linear system. (BICGSTAB ONLY).

8.3.3.26. ICHECK_BICGS

Data Type: INTEGER

Frequency to check for convergence. (BICGSTAB ONLY)

8.3.3.27. OPT_PARALLEL

Data Type: LOGICAL

Sets optimal LEQ flags for parallel runs.

8.3.3.28. USE_DOLOOP

Data Type: LOGICAL

Use do-loop assignment over direct vector assignment.

8.3.3.29. IS_SERIAL

Data Type: LOGICAL

Calculate dot-products more efficiently (Serial runs only.)