IM

IM is an important parameter in the fort.15 file that defines numerical model formulation and dimension. Among other things, IM specifies whether ADCIRC is solved in two-dimensional depth-integrated (2DDI) or in three-dimensions (3D), solution of the governing equations is semi-implicit or explicit in time, and whether the model formulation is barotropic or baroclinic. Popular values for 2D barotropic ADCIRC include IM=0 and IM=111112; users should be aware that the A00, B00, and C00 coefficients must be specified differently in these two cases.

Default IM Values

Default simulation option combinations can be specified through single or double digit values, some of which are shortcuts to the six-digit codes described in the next heading. The available IM values are specified in the table below and in the following section on 6-digit values:

IM Value	Six-digit Equivalent	Description
0	111111	Barotropic 2DDI
1	611111	Barotropic 3D velocity-based momentum
2		Barotropic 3D stress-based momentum
10		Barotropic 2DDI with passive scalar transport
11		Barotropic 3D velocity-based momentum with passive scalar transport
20		Baroclinic 2DDI
21		Baroclinic 3D velocity-based momentum
30		Baroclinic 2DDI with passive scalar transport
31		Baroclinic 3D velocity-based momentum with passive scalar transport

Note that all default IM values employ the semi-implicit consistent GWCE mass matrix solver. It has less numerical error and tends to be more stable than the explicit mass-lumping approach at the expense of computational time and memory.

Six-digit IM Codes

For fine-grained control of various options six-digit codes for IM can be specified. Each digit represents a specific option regarding the dimension and the formulation of certain terms or integration methods in the GWCE or momentum equations. The available options for each digit are specified below, with the first digit being the left-most. The internal flags that are set are listed to help users dig through the code.

Value	Digit 1: 2DDI/3D, Lateral Stress in GWCE [1]	Digit 2: Advection in GWCE [2]	Digit 3: Lateral Stress in Momentum [1]	Digit 4: Advection in Momentum [2]	Digit 5: Area Integration in Momentum	Digit 6: GWCE Mass Matrix, Barotropic/Baroclinic
1 (default)	2DDI, Kolar-Gray flux-based CGWCE_LS_KGQ=.TRUE.	Non conservative CGWCE_Advec_NC=.TRUE.	Integration by parts, velocity-based CME_LS_IBPV=.TRUE.	Non conservative CME_New_NC=.TRUE.	Corrected CME_AreaInt_Corr=.TRUE.	Consistent (implicit for linear part of gravity wave term), barotropic ILump=0
2	2DDI, 2-part flux-based CGWCE_LS_2PartQ=.TRUE.	Conservative form 1 CGWCE_Advec_C1=.TRUE.	Integration by parts, flux-based CME_LS_IBPQ=.TRUE.	Conservative form 1 CME_New_C1=.TRUE.	Original CME_AreaInt_Orig=.TRUE.	Lumped (explicit), barotropic CGWCE_Lump=.TRUE., ILump=1
3	2DDI, 2-part velocity-based CGWCE_LS_2PartV=.TRUE.	Conservative form 2 CGWCE_Advec_C2=.TRUE.	Integration by parts, velocity-based symmetrical CME_LS_IBPSV=.TRUE.	Conservative form 2 CME_New_C2=.TRUE.		Consistent (implicit for full gravity wave term), barotropic CGWCE_HDP=.TRUE., IFNL_HDP=1, ILump=0
4	2DDI, 2-part flux-based symmetrical CGWCE_LS_2PartSQ=.TRUE.		Integration by parts, flux-based symmetrical CME_LS_IBPSQ=.TRUE.
5	2DDI, 2-part velocity-based symmetrical CGWCE_LS_2PartSV=.TRUE.		2 Part, velocity-based (not implemented) CME_LS_2PartV=.TRUE.
6	3D, Kolar-Gray flux-based C2DDI=.FALSE., CGWCE_LS_KGQ=.TRUE., C3D=.TRUE., C3DVS=.TRUE., ILump=0		2 Part, flux-based (not implemented) CME_LS_2PartQ=.TRUE.

A common code combination is IM=111112, which is identical to the default 111111 (same as IM=0), but simulates in explicit mass-lumping mode. Note that A00, B00, and C00 must be set to 0.0 1.0 0.0 when in this mode. Lumped explicit mode is a useful alternative to the (default) semi-implicit consistent GWCE mass matrix mode, because the latter requires a matrix solve that increases computational time and memory. By comparison, the explicit mass-lumping mode is about twice as fast and scales to fewer grid nodes per computational core. [3] Moreover, for model setups that are sufficiently resolved in space and time, differences in the solution between approaches should be small. Though, many users have reported somewhat lower stability in lumped explicit mode.

The most recent version (55+) also has an option that improves the (default) semi-implicit consistent GWCE mass matrix mode to compute the complete (total depth) gravity wave term (free surface gradient) implicitly; toggled by setting IMDigit-6 to 3. The default version (IMDigit-6=1), only computes the initial still water depth component of the free surface gradient implicitly, which might make it more susceptible to CFL violations in shallow depths and can encounter Matrix diagonality issues overland where the initial still water depth is negative.

References

[1] (1,2)

K.M. Dresback, R.L. Kolar, R.A. Luettich, Jr. (2005). On the Form of the Momentum Equation and Lateral Stress Closure Law in Shallow Water Modeling, in: Estuar. Coast. Model., American Society of Civil Engineers, Reston, VA, 399–418. doi:10.1061/40876(209)23

[2] (1,2)

K.M. Dresback, R.L. Kolar, J.C. Dietrich (2005). On the Form of the Momentum Equation for Shallow Water Models Based on the Generalized Wave Continuity Equation: Conservative vs. Non-Conservative. Advances in Water Resources, 28(4), 345-358. doi:10.1016/j.advwatres.2004.11.011

[3]

19. Tanaka, S. Bunya, J.J. Westerink, C. Dawson, R.A. Luettich, Scalability of an Unstructured Grid Continuous Galerkin Based Hurricane Storm Surge Model, J. Sci. Comput. 46 (2011) 329–358. doi:10.1007/s10915-010-9402-1