CMS User Manual i May 2012 Coastal Modeling System Draft User Manual Alejandro Sánchez, Tanya Beck, Lihwa Lin, Zeki Demirbilek, Mitch Brown, and Honghai Li CMS User Manual ii Contents Unit Conversion Factors ............................................................................................................................xiv 1 Introduction ............................................................................................................................................ 1 2 Mathematical Formulations ............................................................................................................... 4 Hydrodynamics ......................................................................................................................... 4 Continuity and Momentum .......................................................................................................... 4 Wave Mass Flux Velocity .............................................................................................................. 6 Mean Wave-Current Bottom Friction ........................................................................................... 7 Wave Radiation Stresses ............................................................................................................. 8 Wind Surface Stress ..................................................................................................................... 9 Eddy Viscosity ............................................................................................................................. 10 Boundary Conditions .................................................................................................................. 13 Sediment Transport ................................................................................................................ 17 Nonequilibrium Total-Load Transport Model ............................................................................ 17 Equilibrium Transport Formulas ................................................................................................ 25 Soulsby-van Rijn Total-load Transport Formula ........................................................................ 34 Hiding and Exposure .................................................................................................................. 36 Horizontal Sediment Mixing Coefficient .................................................................................... 38 Boundary Conditions .................................................................................................................. 38 Salinity Transport.................................................................................................................... 40 Transport Equation .................................................................................................................... 40 Boundary Conditions .................................................................................................................. 40 Surface Roller ......................................................................................................................... 41 Wave Propogation .................................................................................................................. 42 Wave-action Balance Equation with Diffraction ....................................................................... 42 Wave Diffraction ......................................................................................................................... 43 Wave-current Interaction ........................................................................................................... 43 Wave Reflection ......................................................................................................................... 44 Wave Breaking Formulas ........................................................................................................... 45 Wind Forcing and Whitecapping Dissipation ............................................................................ 46 Wave Generation with Arbitrary Wind Direction ....................................................................... 48 Bottom friction loss .................................................................................................................... 50 Wave Runup ............................................................................................................................... 51 Wave Transmission and Overtopping at Structures ................................................................. 53 Variable-rectangular-cell Grid .................................................................................................... 55 Non-linear Wave-wave Interaction ............................................................................................ 55 Wave Dissipation over Muddy Bed ............................................................................................ 56 3 Numerical Methods ............................................................................................................................ 57 Overview ................................................................................................................................. 57 CMS-Flow Computational Grid ............................................................................................... 57 CMS User Manual iii General Transport Equation ................................................................................................... 59 Spatial Discretization ................................................................................................................. 59 Temporal Discretization ............................................................................................................. 60 Cell-face interpolation operator ................................................................................................. 60 Advection Schemes .................................................................................................................... 61 Cell-face gradient operator ........................................................................................................ 62 Cell-centered gradient operator ................................................................................................ 63 Source/sink term ....................................................................................................................... 63 Assembly of Algebraic Equations .............................................................................................. 63 Implicit Relaxation ...................................................................................................................... 64 Iterative Solvers .......................................................................................................................... 64 Convergence and Time Stepping .............................................................................................. 65 Ramp Period ............................................................................................................................... 66 Hydrodynamics ....................................................................................................................... 67 Solution Procedure ..................................................................................................................... 67 Cell-face Velocity ........................................................................................................................ 69 Wetting and Drying ..................................................................................................................... 69 Sediment Transport ................................................................................................................ 71 Transport Equations ................................................................................................................... 71 Mixing Layer ............................................................................................................................... 71 Bed Material Sorting .................................................................................................................. 71 Avalanching ................................................................................................................................ 72 Hard bottom ............................................................................................................................... 73 Semi-Coupling Procedure .......................................................................................................... 73 Surface Roller ......................................................................................................................... 74 Coupling Procedure of CMS-Flow and CMS-Wave ................................................................ 75 Spatial Interpolation and Extrapolation ................................................................................ 77 Water levels ................................................................................................................................ 77 Current Velocities ....................................................................................................................... 77 Bed elevations ............................................................................................................................ 78 Significant