The MIKE software suite consists of 1D (MIKE11) and 2D flexible mesh (MIKE21FM)
components. MIKE11 and MIKE 21FM have been used simulate hydrology, hydraulics, water quality and sediment transport in estuaries, rivers, and other inland waters worldwide
(Edelvang et al. 2002; Havnø, M. N. Madsen, and Dørge 1995;(C. B. Pedersen et al.; Jayatilaka et al., 1998; Niedbala et al., 1999; N. H. Pedersen et al., 2005; Thompson et al., 2004). Both MIKE11 and MIKE 21FM are described in detail below. Model variables, algorithms and their interdependencies of the one- and two-dimensional models and their composite modules are detailed in the DHI, 2010, 2011a, and 2011b.
4.1.1 MIKE11: Hydrodynamic (HD) Module
MIKE11 has a base hydrodynamic module (HD) that uses an implicit, finite difference scheme for the computation of unsteady flow. MIKE 11 simulates changes in water depth and flow velocity in space and time in response to variation in flow rate and/or water surface elevation at boundaries for given bottom morphology and initial conditions. The models provides a full solution of the Saint Venant equations for continuity and momentum (shown below in Equation 1 and Equation 2, respectively), plus many process modules for advection-dispersion (AD), water quality and ecology, sediment transport, and rainfall-runoff.
Equation 1:
+ =
Equation 2
: + + + =
where: q = discharge, Afl = cross section area, qin = lateral inflow (per length unit), h = water level, α = momentum distribution coefficient, If= flow resistance, f= momentum forcing (per length unit), and = density of water.
The module used to simulate the transport of sediment and other non-degrading substances, is based on the one-dimensional equation of conservation of mass of dissolved or suspended material (advection-dispersion equation) as reported in Ariathurai and Krone (1976) and Mehta et al. (1989). The model includes description of sediment settling with different settling
velocities (flocculation), hindered settling and a combination of currents and waves to calculate the bottom shear stress. For the floodplain and river profile, flooded area versus elevation curves are computed to quantify the storage capacity of sections of the floodplain, and are also exported to a MIKE 11 cross-section database.
4.1.2 MIKE11: Advection-Dispersion (AD) Module
The advection-dispersion (AD) module is used to model transport of cohesive sediment, defined as sediments smaller than 63 µm. The CST model solves the advection-dispersion equation, shown in Equation 3:
Equation 3: + ! − # $ % = &'− &(
where Q = discharge, A = cross-sectional flow area, C = cross-sectional average sediment concentration, K = dispersion coefficient, Se = erosion (resuspension) flux, and Sd =deposition flux. Erosional flux is expressed following Equation 4:
Equation 4: &' = )+∗,1 − #../0%12 , 4 ≥ 46'
where M* = erodibility of bed, D = flow depth, U = cross-sectional average flow velocity, and Uce
= critical erosion velocity. Depositional flux is expressed following Equation 5:
Equation 5: &( = +∗ ,1 − #..
/7%12 , 4 ≤ 46(
where w = mean settling velocity of suspended particles, D* = average particle settling depth and Ucd = critical deposition velocity.
The AD module can also simulate the transport, erosion and deposition of non-cohesive sediments based on the one-dimensional equation of conservation of mass of a dissolved or suspended material (i.e. the advection-dispersion equation). The AD module uses as input discharge, water level, cross-sectional area and hydraulic radius output by the HD module. The advection-dispersion equation is solved numerically using an implicit finite difference scheme which is, in principle, unconditionally stable and has negligible numerical dispersion.
4.1.3 MIKE11: Ecolab Xenobiotics Module
Ecolab is a numerical template for ecological and contaminant modeling. The template can be customized to model water quality, eutrophication, heavy metals, organic contaminants and
ecology. The module describes the chemical, biological, ecological processes and interactions between state variables, or variables that describe the mathematical "state" of a dynamic system. State variables included in ECO Lab can either be transported by advection-dispersion processes based on hydrodynamics, or have a more fixed nature (e.g. rooted vegetation).
The transport of xenobiotics discharged into the aquatic environment or from polluted
sediment can be modeled by simulating mechanisms controlling the movement of xenobiotics within the environment. These mechanisms are abundant, but in a macroscopic scale a limited number of overall processes govern transport processes. (Anderson et al., 1987; Honeyman and Santschi, 1988), from (DHI, 2011). These seven processes are listed below:
1. The adsorption and desorption of xenobiotics
2. The sedimentation and resuspension of particle-bound xenobiotics
3. The diffusive transport of dissolved xenobiotics at the sediment/ water interface 4. Biodegradation
5. Photolysis 6. Hydrolysis
7. Evaporation of dissolved xenobiotics
8. The transport of dissolved and particulate xenobiotics in the water column by advection and dispersion.
The xenobiotic ECO Lab template itself accounts for the first seven processes detailed above, while the advection-dispersion process is calculated by MIKE 11. Figure 11 details the
interactions between these processes, in both the sediment and water phases. Appendix B details mathematical formulations behind the Ecolab template.
Figure 11. Processes in the xenobiotics template
4.1.4 MIKE21FM Hydrodynamic Module (HD)
The FM Hydrodynamic Module is based on the numerical solution of the two-dimensional shallow water equations; the depth-integrated incompressible Reynolds averaged Navier-Stokes equations. The model solves equations for continuity, momentum, temperature, salinity and density using a cell-centered finite volume method. The model consists of an unstructured grid composed of triangles or quadrilateral elements in the horizontal plane. An explicit scheme is used for time integration. An approximate Riemann solver is used for computation of
convective fluxes, making discontinuous solutions possible. Manning’s bed roughness and eddy viscosity are the two primary calibration parameters.
Dissolved
4.1.5 MIKE21FM Mud Transport Module (MT)
The Mud Transport (MT) module describes erosion, transport and deposition of mud or sand and mud mixtures under the action of currents and waves. Sand transport can be simulated using this module, but only sand assumed to be transported via suspended transport (i.e.
bedload transport is not simulated). The FM Hydrodynamic module provides the hydrodynamic basis for the MT module. Processes simulated in the model include: morphological update of the bed resulting from erosion and deposition, description of settling processes, flocculation and wave forcing processes. The sediment bed is assumed to be layered and is characterized by its density and shear strength. Dispersion and critical shear stress for deposition are the key parameters for calibration.