Clint Dawson

A Basin- to Channel-Scale Unstructured Grid Hurricane Storm Surge Model Applied to Southern Louisiana

Abstract Southern Louisiana is characterized by low-lying topography and an extensive network of sounds, bays, marshes, lakes, rivers, and inlets that permit widespread inundation during hurricanes. A basin- to channel-scale implementation of the Advanced Circulation (ADCIRC) unstructured grid hydrodynamic model has been developed that accurately simulates hurricane storm surge, tides, and river flow in this complex region. This is accomplished by defining a domain and computational resolution appropriate for the relevant processes, specifying realistic boundary conditions, and implementing accurate, robust, and highly parallel unstructured grid numerical algorithms. The model domain incorporates the western North Atlantic, the Gulf of Mexico, and the Caribbean Sea so that interactions between basins and the shelf are explicitly modeled and the boundary condition specification of tidal and hurricane processes can be readily defined at the deep water open boundary. The unstructured grid enables highly refi...

A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part I: Model Development and Validation

Abstract A coupled system of wind, wind wave, and coastal circulation models has been implemented for southern Louisiana and Mississippi to simulate riverine flows, tides, wind waves, and hurricane storm surge in the region. The system combines the NOAA Hurricane Research Division Wind Analysis System (H*WIND) and the Interactive Objective Kinematic Analysis (IOKA) kinematic wind analyses, the Wave Model (WAM) offshore and Steady-State Irregular Wave (STWAVE) nearshore wind wave models, and the Advanced Circulation (ADCIRC) basin to channel-scale unstructured grid circulation model. The system emphasizes a high-resolution (down to 50 m) representation of the geometry, bathymetry, and topography; nonlinear coupling of all processes including wind wave radiation stress-induced set up; and objective specification of frictional parameters based on land-cover databases and commonly used parameters. Riverine flows and tides are validated for no storm conditions, while winds, wind waves, hydrographs, and high wa...

A High-Resolution Coupled Riverine Flow, Tide, Wind, Wind Wave, and Storm Surge Model for Southern Louisiana and Mississippi. Part II: Synoptic Description and Analysis of Hurricanes Katrina and Rita

Abstract Hurricanes Katrina and Rita were powerful storms that impacted southern Louisiana and Mississippi during the 2005 hurricane season. In Part I, the authors describe and validate a high-resolution coupled riverine flow, tide, wind, wave, and storm surge model for this region. Herein, the model is used to examine the evolution of these hurricanes in more detail. Synoptic histories show how storm tracks, winds, and waves interacted with the topography, the protruding Mississippi River delta, east–west shorelines, manmade structures, and low-lying marshes to develop and propagate storm surge. Perturbations of the model, in which the waves are not included, show the proportional importance of the wave radiation stress gradient induced setup.

Enhanced Cell-Centered Finite Differences for Elliptic Equations on General Geometry

We present an expanded mixed finite element method for solving second-order elliptic partial differential equations on geometrically general domains. For the lowest-order Raviart--Thomas approximating spaces, we use quadrature rules to reduce the method to cell-centered finite differences, possibly enhanced with some face-centered pressures. This substantially reduces the computational complexity of the problem to a symmetric, positive definite system for essentially only as many unknowns as elements. Our new method handles general shape elements (triangles, quadrilaterals, and hexahedra) and full tensor coefficients, while the standard mixed formulation reduces to finite differences only in special cases with rectangular elements. As in other mixed methods, we maintain the local approximation of the divergence (i.e., local mass conservation). In contrast, Galerkin finite element methods facilitate general element shapes at the cost of achieving only global mass conservation. Our method is shown to be as accurate as the standard mixed method for a large class of smooth meshes. On nonsmooth meshes or with nonsmooth coefficients one can add Lagrange multiplier pressure unknowns on certain element edges or faces. This enhanced cell-centered procedure recovers full accuracy, with little additional cost if the coefficients or mesh geometry are piecewise smooth. Theoretical error estimates and numerical examples are given, illustrating the accuracy and efficiency of the methods.

A discontinuous Galerkin method for two-dimensional flow and transport in shallow water

Abstract A discontinuous Galerkin (DG) finite element method is described for the two-dimensional, depth-integrated shallow water equations (SWEs). This method is based on formulating the SWEs as a system of conservation laws, or advection–diffusion equations. A weak formulation is obtained by integrating the equations over a single element, and approximating the unknowns by piecewise, possibly discontinuous, polynomials. Because of its local nature, the DG method easily allows for varying the polynomial order of approximation. It is also “locally conservative”, and incorporates upwinded numerical fluxes for modeling problems with high flow gradients. Numerical results are presented for several test cases, including supercritical flow, river inflow and standard tidal flow in complex domains, and a contaminant transport scenario where we have coupled the shallow water flow equations with a transport equation for a chemical species.

An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions

Abstract In this paper we develop an unsplit, higher order Godunov method for scalar conservation laws in two dimensions. The method represents an extension, for the special case being considered, of methods developed by Colella and by Van Leer. In our method we begin with a piecewise bilinear representation of the solution on each grid cell. A new piecewise bilinear representation at the next time level is then obtained from a two-step procedure. In the first step, a conservative predictor-corrector scheme derived from the integral form of the differential equation and characteristic considerations is used to obtain average values of the solution over grid cells at the new time level. Next, these new average values are then used to construct a limited, piecewise bilinear profile for each cell at the new time level. The resulting method is shown to satisfy a maximum principle for constant coefficient linear advection. Computational results are presented comparing the new method to Colellas method for linear advection. The method is also applied to two model problems from porous media flow, miscible and immiscible displacement. The new scheme provides accurate resolution of sharp fronts without any significant distortion.

Hurricane Gustav (2008) Waves and Storm Surge: Hindcast, Synoptic Analysis, and Validation in Southern Louisiana

AbstractHurricane Gustav (2008) made landfall in southern Louisiana on 1 September 2008 with its eye never closer than 75 km to New Orleans, but its waves and storm surge threatened to flood the city. Easterly tropical-storm-strength winds impacted the region east of the Mississippi River for 12–15 h, allowing for early surge to develop up to 3.5 m there and enter the river and the city’s navigation canals. During landfall, winds shifted from easterly to southerly, resulting in late surge development and propagation over more than 70 km of marshes on the river’s west bank, over more than 40 km of Caernarvon marsh on the east bank, and into Lake Pontchartrain to the north. Wind waves with estimated significant heights of 15 m developed in the deep Gulf of Mexico but were reduced in size once they reached the continental shelf. The barrier islands further dissipated the waves, and locally generated seas existed behind these effective breaking zones.The hardening and innovative deployment of gauges since Hur...

Performance of the Unstructured-Mesh, SWAN+ADCIRC Model in Computing Hurricane Waves and Surge

Coupling wave and circulation models is vital in order to define shelf, nearshore and inland hydrodynamics during a hurricane. The intricacies of the inland floodplain domain, level of required mesh resolution and physics make these complex computations very cycle-intensive. Nonetheless, fast wall-clock times are important, especially when forecasting an incoming hurricane.We examine the performance of the unstructured-mesh, SWAN+ADCIRC wave and circulation model applied to a high-resolution, 5M-vertex, finite-element SL16 mesh of the Gulf of Mexico and Louisiana. This multi-process, multi-scale modeling system has been integrated by utilizing inter-model communication that is intra-core. The modeling system is validated through hindcasts of Hurricanes Katrina and Rita (2005), Gustav and Ike (2008) and comprehensive comparisons to wave and water level measurements throughout the region. The performance is tested on a variety of platforms, via the examination of output file requirements and management, and the establishment of wall-clock times and scalability using up to 9,216 cores. Hindcasts of waves and storm surge can be computed efficiently, by solving for as many as 2.3⋅1012 unknowns per day of simulation, in as little as 10 minutes of wall-clock time.

Godunov-mixed methods for advection-diffusion equations in multidimensions

Time-split methods for multidimensional advection-diffusion equations are considered. In these methods, advection is approximated by a Godunov-type procedure, and diffusion is approximated by a low...

Godunov-mixed methods for advective flow problems in one space dimension

A time-splitting method for solving advection-dominated, parabolic, partial differential equations is presented. In this method, a higher-order Godunov procedure approximates advection and a mixed finite element procedure approximates diffusion. Several variations on the basic scheme are formulated for solving one-dimensional, quasilinear, parabolic problems with Dirichlet boundary conditions. A maximum principle for one variant of the scheme is demonstrated, and