Numerical Modelling of the 26th December 2004 Indian Ocean Tsunami for the Southeastern Coast of India

A numerical simulation of the 26th December, 2004 Indian Ocean tsunami of the Tamil Nadu coastal zone is presented. The simulation approach is based on a fully nonlinear Boussinesq tsunami propagation model and included an accurate computational domain and a robust coseismic source. The simulation is first confronted to available tide gauge and runup observations. The agreement between observations and the predicted wave heights allowed a reasonable validation of the simulation. As a result, a full picture of the tsunami impact is provided over the entire coastal zone Tamil Nadu. The processes responsible for coastal vulnerability are discussed.     

Dynamic responses of coastal structures during earthquakes including sediment–sea–structure interaction

The effects of the interaction among sea water, sediment, backfill-soil and coastal structures (embankments) were included in the present study. The formulation is derived from fundamental theories in various fields, including marine hydrodynamics, flow in porous medium, and structural dynamics. The hybrid finite-difference and finite element methods were used in the analysis. The finite-difference method was used to calculate the nonlinear hydrodynamic pressures of sea water as well as the pore water in the sediment acting on the coastal embankment faces by seismic-wave actions. The fluid-filled solid mixture was used to model sediment and back-fill soil and the corresponding dynamic responses were also evaluated by finite difference method. The dynamic response of the coastal structures was calculated by finite element method. The numerical results are presented for various water depths and ground motion intensities. The significant dynamic forces on coastal structures were calculated during earthquakes and the possible sliding of the coastal embankment will occur and the special foundation treatment should be made.     

A numerical study of the effect of the marginal sea on coastal upwelling in a non-linear inertial model

Inertia theory and the finite element method are used to investigate the effect of marginal seas on coastal upwelling. In contrast to much previous research on wind-driven upwelling, this paper does not consider localized wind effects, but focuses instead on temperature stratification, the slope of the continental shelf, and the background flow field. Finite element method, which is both faster and more robust than finite difference method in solving problems with complex boundary conditions, was developed to solve the partial differential equations that govern coastal upwelling. Our results demonstrate that the environment of the marginal sea plays an important role in coastal upwelling. First, the background flow at the outer boundary is the main driving force of upwelling. As the background flow strengthens, the overall velocity of cross-shelf flow increases and the horizontal scale of the upwelling front widens, and this is accompanied by the movement of the upwelling front further offshore. Second, temperature stratification determines the direction of cross-shelf flows, with strong stratification favoring a narrow and intense upwelling zone. Third, the slope of the continental shelf plays an important role in controlling the intensity of upwelling and the height that upwelling may reach: the steeper the slope, the lower height of the upwelling. An additional phenomenon that should be noted is upwelling separation, which occurs even without a local wind force in the nonlinear model.     

Simplified nonlinear modeling of river flow routing

Management of open-channel flow systems requires accurate models of flow transfer. This article presents a simple nonlinear model representative of the flow transfer in a river reach. The model is obtained through linearization of a physical model, simplification using the cumulant matching method and analytic identification of a nonlinear model coinciding with the linear model around equilibrium points, corresponding to the hydraulic permanent regimes. The methodology is illustrated on the diffusive wave equation and the Saint-Venant equations. The obtained nonlinear models are compared in simulation to the initial models. The nonlinear model is shown to ensure mass conservation, despite the variable delay element of the model. The proposed model can reproduce the nonlinear behavior of the time-delay with discharge variations. It is well-suited for fast simulations, flow forecasting, and for controller design.     

The influence of a coastal headland on oceanic boundary currents

Abstract

The steady state circulation of a constant barotropic current around a coastal headland, bay, or combination of the two, located on a flat bottom, mid-latitude β-plane is considered. The maximum displacement of the coastal features from the mean straight coastline is assumed to be small compared to the longshore variation of the coastline. Under this slowly varying coastline approximation, a linearised vorticity equation is derived for the perturbation stream function. An analytical solution for the perturbation stream function is obtained using a Green's function technique. For a specified coastline the effects of coastal orientation, linear friction and the strength of the mean flow are investigated. The model predicts that the flow field will adopt the pattern of the coastline. The question of whether a coastal feature is likely to induce linear flow dynamics within the coastal boundary layer is also addressed. In the case when a single Gaussian headland or bay violates the slowly varying longshore condition the model predicts that flow stagnation will not occur. However for multiple headlands and bays, flow stagnation is possible when the slowly varying longshore condition is sufficiently violated.

Cape Mendocino and Point Conception along the California coast can be modelled using either a single Gaussian headland coastline or a multiple headland and bay coastline. In either case the model coastline does not vary slowly alongshore and nonlinear flow in the coastal region is likely. A permanent eddy to the south of Point Conception is likely to testify to the non-linear flow regime induced by the headland.     

Nonlinear Flow Process: A New Package to Compute Nonlinear Flow in MODFLOW

A new MODFLOW package (Nonlinear Flow Process; NLFP) simulating nonlinear flow following the Forchheimer equation was developed and implemented in MODLFOW‐2005. The method is based on an iterative modification of the conductance calculated and used by MODFLOW to obtain an effective Forchheimer conductance. The package is compatible with the different layer types, boundary conditions, and solvers as well as the wetting capability of MODFLOW. The correct implementation is demonstrated using four different benchmark scenarios for which analytical solutions are available. A scenario considering transient flow in a more realistic setting and a larger model domain with a higher number of cells demonstrates that NLFP performs well under more complex conditions, although it converges moderately slower than the standard MODFLOW depending on the nonlinearity of flow. Thus, this new tool opens a field of opportunities to groundwater flow simulation with MODFLOW, especially for core sample simulation or vuggy karstified aquifers as well as for nonlinear flow in the vicinity of pumping wells.     

A semi-analytical time integration for numerical solution of Boussinesq equation

A semi-analytical time integration method is proposed for the numerical simulation of transient groundwater flow in unconfined aquifers by the nonlinear Boussinesq equation. The method is based on the analytical solution of the system of ordinary differential equations with constant coefficients. While it is unconditionally stable and more accurate than the finite difference methods, the computational cost is much more expensive than (can be more than 10 times) that of the finite difference methods for a single time step. However, by partitioning the nonlinear parameters into linear and nonlinear parts, the costly computation can be performed only once. With larger and less variable time step sizes, the total computational cost can be significantly reduced. Three examples are included to illustrate the advantages and limitations of the proposed method.     

Flow imaging method of electromagnetic measurement in well logging

Multiphase flow in an oil well is a dynamic phenomenon of inhomogeneous medium,which should be studied in a nonlinear way. This paper presents an electromagnetic measurement method based on the electrical property differences between oil,gas and water to scan,inverse and show the distribution and condition of multiphase flow. Both numerical simulation and physical experiments have proved that clear images could be obtained by this way.     

NEW TRENDS IN THE NUMERICAL STUDY OF COASTAL SEDIMENTARY PROCESSES

1 INTRODUCTION The conventional method for numerical study of coastal sedimentary processes has been based on the solution of a phase-averaged wave equation, the steady nearshore current equations, the continuity equation for sediment, and an empirical net sediment transport equation. This strategy has advantages in meso-scale problems but it loses accuracy in the vicinity of a structure, where local scour usually occurs. To have a good representation of both meso-scale sediment transport …     

Effects of macro-pores on water flow in coastal subsurface drainage systems

Leaching through subsurface drainage systems has been widely adopted to ameliorate saline soils. The application of this method to remove salt from reclaimed lands in the coastal zone, however, may be impacted by macro-pores such as crab burrows, which are commonly distributed in the soils. We developed a three-dimensional model to investigate water flow in subsurface drainage systems affected by macro-pores distributed deterministically and randomly through Monte Carlo simulations. The results showed that, for subsurface drainage systems under the condition of continuous surface ponding, macro-pores increased the hydraulic head in the deep soil, which in turn reduced the hydraulic gradient between the surface and deep soil. As a consequence, water infiltration across the soil surface was inhibited. Since salt transport in the soil is dominated by advection, the flow simulation results indicated that macro-pores decreased the efficiency of salt leaching by one order of magnitude, in terms of both the elapsed time and the amount of water required to remove salt over the designed soil leaching depth (0.6 m). The reduction of the leaching efficiency was even greater in drainage systems with a layered soil stratigraphy. Sensitivity analyses demonstrated that with an increased penetration depth or density of macro-pores, the leaching efficiency decreased further. The revealed impact of macro-pores on water flow represents a significant shortcoming of the salt leaching technique when applied to coastal saline soils. Future designs of soil amelioration schemes in the coastal zone should consider and aim to minimize the bypassing effect caused by macro-pores.     

Solution of the nonlinear transport equation using modified Picard iteration

The transport and fate of reactive chemicals in groundwater is governed by equations which are often difficult to solve due to the nonlinear relationship between the solute concentrations for the liquid and solid phases. The nonlinearity may cause mass balance errors during the numerical simulation in addition to numerical errors for linear transport system. We have generalized the modified Picard iteration algorithm of Celia et al.⁵ for unsaturated flow to solve the nonlinear transport equation. Written in a ‘mixed-form’ formulation, the total solute concentration is expanded in a Taylor series with respect to the solution concentration to linearize the transport equation, which is then solved with a conventional finite element method. Numerical results of this mixed-form algorithm are compared with those obtained with the concentration-based scheme using conventional Picard iteration. In general, the new solver resulted in negligible mass balance errors (< ∥10⁻⁸∥%) and required less computational time than the conventional iteration scheme for the test examples, including transport involving highly nonlinear adsorption under steady-state as well as transient flow conditions. In contrast, mass balance errors resulting from the conventional Picard iteration method were higher than 10% for some highly nonlinear problems. Application of the modified Picard iteration scheme to solve the nonlinear transport equation may greatly reduce the mass balance errors and increase computational efficiency.     

A Method for Evaluating Flow Characteristics in the Coastal Zone

The main factors that control flow characteristics in the coastal zone are discussed. A method is proposed for evaluating flow characteristics and wave transformation.     

A new approach for phase transitions in miscible multi-phase flow in porous media

The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if miscibility is also considered. A primary reason why inclusion of miscibility tends to be problematic are the difficulties stemming from phase transitions: on the one hand, phase transitions need to be included since the presence or absence of fluid phases has a major impact on the flow behavior; on the other hand, convergence of the nonlinear solver may be severely affected if they are not handled robustly.In this work, we present a mathematically sound approach to include phase transitions in the nonlinear system of equations: first, the transition conditions are formulated as a set of local inequality constraints, which are then directly integrated into the nonlinear solver using a nonlinear complementarity function. Under this scheme, Newton-Raphson solvers exhibit considerably more robust convergence behaviour compared to some previous approaches, which is then illustrated by several numerical examples.     

MODFLOW‐Based Coupled Surface Water Routing and Groundwater‐Flow Simulation

In this paper, we present a flexible approach for simulating one‐ and two‐dimensional routing of surface water using a numerical surface water routing (SWR) code implicitly coupled to the groundwater‐flow process in MODFLOW. Surface water routing in SWR can be simulated using a diffusive‐wave approximation of the Saint‐Venant equations and/or a simplified level‐pool approach. SWR can account for surface water flow controlled by backwater conditions caused by small water‐surface gradients or surface water control structures. A number of typical surface water control structures, such as culverts, weirs, and gates, can be represented, and it is possible to implement operational rules to manage surface water stages and streamflow. The nonlinear system of surface water flow equations formulated in SWR is solved by using Newton methods and direct or iterative solvers. SWR was tested by simulating the (1) Lal axisymmetric overland flow, (2) V‐catchment, and (3) modified Pinder‐Sauer problems. Simulated results for these problems compare well with other published results and indicate that SWR provides accurate results for surface water‐only and coupled surface water/groundwater problems. Results for an application of SWR and MODFLOW to the Snapper Creek area of Miami‐Dade County, Florida, USA are also presented and demonstrate the value of coupled surface water and groundwater simulation in managed, low‐relief coastal settings.     

Analytic Element Modeling of Steady Interface Flow in Multilayer Aquifers Using AnAqSim

This paper presents the analytic element modeling approach implemented in the software AnAqSim for simulating steady groundwater flow with a sharp fresh‐salt interface in multilayer (three‐dimensional) aquifer systems. Compared with numerical methods for variable‐density interface modeling, this approach allows quick model construction and can yield useful guidance about the three‐dimensional configuration of an interface even at a large scale. The approach employs subdomains and multiple layers as outlined by Fitts (2010) with the addition of discharge potentials for shallow interface flow (Strack 1989). The following simplifying assumptions are made: steady flow, a sharp interface between fresh‐ and salt water, static salt water, and no resistance to vertical flow and hydrostatic heads within each fresh water layer. A key component of this approach is a transition to a thin fixed minimum fresh water thickness mode when the fresh water thickness approaches zero. This allows the solution to converge and determine the steady interface position without a long transient simulation. The approach is checked against the widely used numerical codes SEAWAT and SWI/MODFLOW and a hypothetical application of the method to a coastal wellfield is presented.     

Screening of one-well hydraulic barrier design alternatives

This study develops a robust method for screening one-well hydraulic barrier design alternatives that can be easily computed without a numerical simulation model. The paper outlines the general method and shows its implementation with hydraulic barriers using a single pumping well. For such barriers, the method is easily computable with spreadsheets and/or charts depicted within the paper and posted online. The method applies the potential flow theory, which leads to using a curvilinear coordinate system for all types of calculations. For contaminant transport calculations, the method applies the boundary layer theory. For calculations of aquifer remediation, the method refers to bulk characteristics of the domain. As an example, the method has been applied to calculate the possible containment of a wide part of the coastal plain aquifer in Israel, which is contaminated by entrapped kerosene (a light nonaqueous phase liquid).     

Seasonal flows of international British Columbia-Alaska rivers: The nonlinear influence of ocean-atmosphere circulation patterns

The northern portion of the Pacific coastal temperate rainforest (PCTR) is one of the least anthropogenically modified regions on earth and remains in many respects a frontier area to science. Rivers crossing the northern PCTR, which is also an international boundary region between British Columbia, Canada and Alaska, USA, deliver large freshwater and biogeochemical fluxes to the Gulf of Alaska and establish linkages between coastal and continental ecosystems. We evaluate interannual flow variability in three transboundary PCTR watersheds in response to El Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), Arctic Oscillation (AO), and North Pacific Gyre Oscillation (NPGO). Historical hydroclimatic datasets from both Canada and the USA are analyzed using an up-to-date methodological suite accommodating both seasonally transient and highly nonlinear teleconnections. We find that streamflow teleconnections occur over particular seasonal windows reflecting the intersection of specific atmospheric and terrestrial hydrologic processes. The strongest signal is a snowmelt-driven flow timing shift resulting from ENSO- and PDO-associated temperature anomalies. Autumn rainfall runoff is also modulated by these climate modes, and a glacier-mediated teleconnection contributes to a late-summer ENSO-flow association. Teleconnections between AO and freshet flows reflect corresponding temperature and precipitation anomalies. A coherent NPGO signal is not clearly evident in streamflow. Linear and monotonically nonlinear teleconnections were widely identified, with less evidence for the parabolic effects that can play an important role elsewhere. The streamflow teleconnections did not vary greatly between hydrometric stations, presumably reflecting broad similarities in watershed characteristics. These results establish a regional foundation for both transboundary water management and studies of long-term hydroclimatic and environmental change.     

Modeling plume behavior for nonlinearly sorbing solutes in saturated homogeneous porous media

Transport of a sorbing solute in a two-dimensional steady and uniform flow field is modeled using a particle tracking random walk method. The solute is initially introduced from an instantaneous point source. Cases of linear and nonlinear sorption isotherms are considered. Local pore velocity and mechanical dispersion are used to describe the solute transport mechanisms at the local scale. The numerical simulation of solute particle transport yields the large scale behavior of the solute plume. Behavior of the plume is quantified in terms of the center-of-mass displacement distance, relative velocity of the center-of-mass, mass breakthrough curves, spread variance, and longitudinal skewness. The nonlinear sorption isotherm affects the plume behavior in the following way relative to the linear isotherm: (1) the plume velocity decreases exponentially with time; (2) the longitudinal variance increases nonlinearly with time; (3) the solute front is steepened and tailing is enhanced     

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.