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# 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.

## 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 below:

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 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:

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 Non conservative Integration by parts, velocity-based Non conservative Corrected Consistent (semi-implicit), barotropic
2 2DDI, 2-part flux-based Conservative form 1 Integration by parts, flux-based Conservative form 1 Original Lumped (explicit), barotropic
3 2DDI, 2-part velocity-based Conservative form 2 Integration by parts, velocity-based symmetrical Conservative form 2 - Lumped (explicit), baroclinic (not yet implemented in ADCIRC release version)
4 2DDI, 2-part flux-based symmetrical - Integration by parts, flux-based symmetrical - - -
5 2DDI, 2-part velocity-based symmetrical - 2 Part, velocity-based (not implemented) - - -
6 3D, Kolar-Gray flux-based - 2 Part, flux-based (not implemented) - - -

A common code combination is IM = 111112, which uses default options (same as IM = 0), but simulates in explicit mass-lumping mode. This is a useful alternative to the (default) semi-implicit consistent GWCE mass matrix mode, which requires a matrix solve increasing computational time and memory compared to the explicit mass-lumping mode, which as 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 negligible.

## References

1. 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. 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. S. 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