Nikolaos D. Katopodes

A numerical model of channel inception on submarine fans

The most common type of submarine fan is created by the passage of a succession of depositional turbidity currents. It is thus of interest to note that even in this essentially depositional environment the fan surface is often intensely channelized. Here a two-dimensional numerical model describing the formation of a submarine fan by a spreading turbidity current is presented. Layer-averaged governing equations describing the turbidity current are presented and solved numerically in conjunction with the Exner equation of bed sediment continuity. The formulation describes fan evolution from an initially flat surface. The bed is allowed to evolve in response to the exchange of sediment with the turbidity current by means of simultaneous erosion and deposition of suspended sediment. The upstream boundary condition is chosen so as to approximate a submarine canyon debouching upon the fan. Under some but not all conditions the early stage of the depositional process is accompanied by the formation of incipient natural levees that act to partially channelize the flow, indicating the formation of a channel-levee system. Dimensionless parameters are used to describe conditions for optimal channelization. The model can explain some of the basic mechanisms that account for the persistent tendency for channelization of the fan surface under a wide range of conditions.

The anti-dissipative, non-monotone behavior of Petrov-Galerkin upwinding

SUMMARY The Petrov‐Galerkin method has been developed with the primary goal of damping spurious oscillations near discontinuities in advection dominated flows. For time-dependent problems, the typical Petrov‐ Galerkin method is based on the minimization of the dispersion error and the simultaneous selective addition of dissipation. This optimal design helps to dampen the oscillations prevalent near discontinuities in standard Bubnov‐Galerkin solutions. However, it is demonstrated that when the Courant number is less than 1, the Petrov‐Galerkin method actually amplifies undershoots at the base of discontinuities. This is shown in an heuristic manner, and is demonstrated with numerical experiments with the scalar advection and Richards’ equations. A discussion of monotonicity preservation as a design criterion, as opposed to phase or amplitude error minimization, is also presented. The Petrov‐Galerkin method is further linked to the high-resolution, total variation diminishing (TVD) finite volume method in order to obtain a monotonicity preserving Petrov‐Galerkin method. Copyright

Self-adaptive kinematic-dynamic model for overland flow

AbstractThe authors developed an innovative two-dimensional finite-volume model for overland flow, which is capable of simultaneously applying the kinematic wave approximation and the full Saint-Venant (dynamic) equations to different regions of the modeled domain. A locally based criterion is employed to determine the applicability limits for the kinematic approximation. The model assesses the flow and topography on a cell-by-cell basis at each time step over an unstructured, triangular grid and determines the appropriate solution method for each individual cell. Several case studies are shown that illustrate the adaptive kinematic-dynamic model’s flexibility and robustness. The effects of the user-defined limit for the kinematic wave approximation and the abrupt switch from one solver to another are explored for the adaptive kinematic-dynamic model.

Hydrodynamics of surface irrigation: vertical structure of the surge front

A model for surface irrigation is developed that allows the determination of the vertical structure of the velocity profile in the vicinity of the wave front. The pressure is not assumed to be hydrostatically distributed and no assumptions are made regarding the shape of the freesurface profile. The turbulent kinetic energy and rate of dissipation are computed by a two-equation model and accurate determination of the bottom shear makes possible the analysis of particle suspension. The model is based on a two-dimensional finite element model in the vertical plane and uses the kinematic condition for determining the position of the free surface. It also incorporates a numerical technique for describing surface penetration and wave breaking by combining a Lagrangian approach that allows the computational nodes to move individually and then automatically reshapes the element grid. The potential value of the model lies in its ability to provide information on vertical mixing, settling and suspension of contaminated solids commonly found in irrigation applications.

Control of sudden releases in channel flow

We present a method for the detection and real-time control of chemical releases in channel flow. Sensor arrays capable of detecting a broad menu of chemical agents are required at strategic locations of the channel. The sensors detect the instantaneous, spatially distributed concentration of the chemical agent and transmit the associated information to a predictive control model. The model provides optimal operation scenarios for computer controlled bleed valves mounted on the channel walls and connected to a common manifold. Control and elimination of the chemical cloud are achieved by optimal blowing and suction of ambient fluid. Gradient information is obtained by use of adjoint equations, so optimization of the control actions is achieved with the highest possible efficiency. The control is optimized over a finite prediction horizon and instructions are sent to the valve manifold. Next, the sensor arrays detect all changes effected by the control and report them to the control model, which advances the process over the next control horizon. Non-reflective boundary conditions for the adjoint equations are derived by a characteristic analysis, which minimizes spurious information in the computation of sensitivities.

Impact of high-resolution modeling on secondary flow phenomena

A high-resolution hydrodynamic model is used to demonstrate that small variations of coefficients in nonlinear filters used to preserve the monotonicity of the solution can lead to significant changes in the computed results. The model is applied to a complex geometry and bathymetry environment, which further aggravate the computational differences. Thermal plumes from hypothetical tests in Green Bay are shown to assume entirely different configurations following long runs of the model. The dissipative nature of various filters is found to alter dramatically not only the spurious oscillations, but the underlying smooth solution of the problem.

Control of Pollutants in the Trans-Boundary Area of Taihu Basin, Yangtze Delta

This work focuses on pollution control in the trans-boundary area of Taihu Basin. Considering the unique characteristics of the river network in the study area, a new methodology of pollution control is proposed aiming at improving the water quality in the trans-boundary area and reducing conflicts between up and downstream regions. Based on monitoring data and statistical analysis, important trans-boundary cross sections identified by the regional government were selected as important areas for consideration in developing management objectives; using a 1-D mathematicmodel and an effective weight evaluation model, the trans-boundary effective control scope (TECS) of the study area was identified as the scope for pollutant control; the acceptable pollution load was then estimated using an established model targeting bi-directional flow. The results suggest that the water environmental capacity for chemical oxygen demand (COD), in order to guarantee reaching the target water quality standard in the TECS, is 160,806 t/year, and amounts to 16,098 t/year, 3493 t/year, and 39,768 t/year for ammonia nitrogen, total nitrogen, and total phosphorus, respectively. Our study method and results have been incorporated into the local government management project, and have been proven to be useful in designing a pollution control strategy and management policy.

Initial findings on the feasibility of real-time feedback control of a hazardous contaminant released into channel flow by means of a laboratory-scale physical prototype

The threat of accidental or deliberate toxic chemicals released into public spaces is a significant concern to public safety. The real-time detection and mitigation of such hazardous contaminants has the potential to minimize harm and save lives. We develop a computational fluid dynamics (CFD) flow control model with the capability of detecting and mitigating such contaminants. Furthermore, we develop a physical prototype to then test the computer model. The physical prototype is in its final stages of construction. Its current state, along with preliminary examples of the flow control model are presented throughout this paper.Copyright

Model development for real time optimal control in pipe lines

A model reference optimal control architecture for the real-time fluid control of eliminating a contaminant plume from a pipe system was introduced in an earlier paper [1]. The mathematical model for the contaminant flow, is now extended and parameterized based on computational fluid dynamic simulations of a two-dimensional (2D) channel. It is also shown, based on the computational fluid dynamics (CFD) simulations, that the 2D-based mathematical model can be used for three-dimensional (3D) pipe flow problem under certain constraints. Finally, we also derive a very simple control law of the flow rate in a boundary port that would remove a contaminant if the flow was a theoretical 2D flow. This simple control law can initialize the iterative process of computing the optimal flow based on a more complex model and real-time measurements. With the results in this article, the optimal control architecture can be tested in the real-time prototype experiments. Further improvements on the mathematical model and control algorithm can be made for real life pipe-line fluid control problems.

Nested grid models for ocean processes

This paper presents a novel two-way nested grid scheme that allows information to travel freely through the computational boundaries of the grid interface. The method tentatively assumes the pressure boundary conditions between subdomains, but uses a receding boundary approach to minimize the pressure errors. Initially, the domains overlap, but within a few time steps the overlap is eliminated by the receding boundaries, so repeated use of approximate boundary conditions is avoided. This prevents the accumulation of errors on the subdomain boundaries and, furthermore, decreases the transfer of errors to the rest of the domain by continuously discarding boundary data. To avoid continuous shrinking of the subdomains, the boundaries are reset to their original positions every few time steps. Successful applications of the method are presented for surface wave propagation, gravity currents and a combination of both surface and internal waves.Copyright