Hydrodynamic Modeling at the University of Oklahoma
	Research Topics We hope you got a feeling for Hydrodynamic Modeling from the Research Q & A section. In this space, we hope to give you a better idea of some of the specific areas of our research. Development Hydrodynamic Modeling involves the simulation of water behavior in oceans, lakes, estuaries, etc. In order to do this, we must convert the infinite-dimensional real world into a finite-dimensional computer world. This conversion requires contributions from three fields: Physics It is important to capture the physics of water behavior, which relies on a wide range of factors: tides, density differences, wind, bathymetry, etc. The ADCIRC model uses the shallow water equations, specifically the conservation of mass (Generalized Wave Continuity Equation) and the conservation of momentum. Research continues to examine the strengths and weaknesses of these equations and determine the situations in which they should be applied. Numerics The ocean can be thought of as an infinite number of points, each with its own elevation and velocity. Numerical methods allow us to model this infinite system on a finite machine. The ADCIRC model uses the Galerkin finite element method, which breaks the domain into triangles. We solve for the elevation and velocity at the three nodes of each triangle. This method allows us to model shorelines, where we can use smaller triangles to capture the shape of the coast. Research continues to examine how we can best implement this method. Computation It is also important to maximize our computational efficiency. Simulations can become very large; for example, storm surge simulations in the New Orleans area can require grids with more than 200,000 nodes. These large problems can take a long time to run on one computer, so we spread out the work through the use of high performance computing. (Please see the Facilities section for more information on our cluster.) By spreading a simulation over multiple computers, we can run it in a shorter time. This has obvious advantages in situations like the New Orleans storm surge example, where time can save lives and property. Research continues to examine how we can best implement our model in a parallel computing environment. Application Once the model is developed, we can apply it to simulate water behavior in oceans, lakes, estuaries, etc. The ADCIRC model has a variety of applications. Weather forecasters use it to predict storm surge inundations. Oceanographers use it to produce tidal charts and study circulation patterns in near-shore and oceanic waters. The government uses it to coordinate naval fleet operations. Marine biologists use it to simulate larvae movement in estuaries and inlets along the coast, in order to measure the effects of man-made shipping channels. Testing However, before we can be sure that the model is mirroring reality, we must subject it to a number of tests: Accuracy We must not lose touch with the real-world behavior that we are modeling. The model's accuracy must be tested. This can be done in a variety of ways: we can compare model results with real data; we can compare model results with an analytical solution; or we can perform convergence studies on the model itself. Because we do not always have real data or an analytical solution, we often use convergence studies. As the time step or the grid spacing is reduced, the model's error should converge to zero. Stability Accuracy alone is not sufficient; the model must also be stable. We must be able to take sizeable time steps without getting erroneous results. This is important information to have, as it helps users to understand how run-time conditions can affect the model's behavior. Sensitivity Hydrodynamic models reflect the complexities of the systems that they simulate. The input files can be several pages in length, as users have to specify values for a wide range of physical and numerical parameters. It is important to know how these parameters affect the performance of the model. Sensitivity tests single out each parameter and study their effects. Like stability tests, these sensitivity studies provide information that is necessary to run the model. Mass Balance One of the drawbacks of the finite element method is its poor mass balance properties. Thus, whenever a change is made to the model, its effects on mass conservation must be understood. Research continues to examine just how poor the method's properties are.