Mitigation of Local Tsunami Effects
(Three-Dimensional Simulation of Wave Interaction
with Solid and Porous Structures)

Project Summary

When earthquakes or landslides occur on ocean floors, they set in motion the entire water column above the affected region, resulting in long-wavelength waves that proceed to strike on surrounding shores. These waves, called tsunamis, can reach more than ten meters in height and can cause extensive destruction and even significant loss of human lives. Since the propagation speed of a tsunami, which is determined by the local water depth, can exceed 700 km/hr, tsunamigenic events can leave very little time for evacuation and mitigation efforts. It is therefore critical to advance the capability of modeling tsunamis for the purposes of predicting arrival times and describing wave interactions with structures upon landfall. Based on the collective experiences of the team of investigators in numerical modeling, laboratory measurements, and surveying of actual tsunami events, a comprehensive research program is proposed to understand local tsunami effects on man-made and natural structures. The research will place particular emphasis on understanding tsunami-structure interactions that can lead to effective measures for damage mitigation. The proposed computational, experimental, and mitigation components are conducted by a research team of eight principal investigators (PIs) located at six US institutions. The tasks are distributed so as to avoid unnecessary duplication and to utilize the special strengths and talents of each of the PIs. Yet, each task is closely related to the others such that common research components must be worked on collectively among the PIs. Professor George Carrier of Harvard University will work on the analytical approach with Professor Harry Yeh of University of Washington. Professor Peter Raad of Southern Methodist University, Professor Costas Synolakis of the University of Southern California, and Professor Philip Liu of Cornell University will undertake different aspects of the numerical modeling. Professors Harry Yeh and Catherine Petroff of University of Washington and Professor Edwin Cowen of Cornell University will design and conduct the laboratory experiments. Ms. Jane Preuss of Urban Regional Research at Seattle will provide realistic scenario mitigation measures related to the joint research activities. The work at SMU will focus on the continued development of computational techniques for the numerical simulation of waves and their interactions with coastal structures. Coupled with the direct field experience of URR in the assessment of tsunami damage and the identification of vulnerability patterns, the collaborative computational and experimental research efforts will enable the development of tsunami mitigation measures. Throughout the research, full advantage will be taken of the multi-disciplinary nature of the research team. The analyses of actual tsunami events will guide the numerical and experimental efforts by focusing the proposed investigations on the most practical and relevant problems for tsunami hazard reduction. The intended, primary impact of the proposed research is the mitigation of the devastating consequences of tsunami events, including loss of human life, destruction of property, damage to the environment, economic disruption, and social dislocation.

Summary of Results

This is a comprehensive research program that is aimed at understanding local tsunami effects on man-made and natural structures, and is guided by the ultimate goal of helping devise measures for effective damage mitigation. The understanding of the fluid-solid interactions require that the fluid dynamics simulation technique be able to deal with three-dimensional effects, curvilinear boundaries, and moving solids. At the onset of the work, the surface marker and micro cell simulation technique, previously developed at SMU, was two-dimensional, could deal with stationary structures, and could only represent solid geometries with rectangular cells, resulting in inaccurate stair-step representations of curvilinear surfaces. Consequently, three parallel efforts were undertaken to develop:

1. a fully three-dimensional surface marker and micro cell computational method,
2. a capability to represent curvilinear boundaries within a Cartesian grid system,
3. a capability to deal with arbitrarily moving boundaries.

The first goal has been achieved with the development and validation of the three-dimensional Eulerian-Lagrangian Marker and Micro Cell (ELMMC-3D) technique, which is capable of simulating incom-pressible fluid flow problems in Cartesian coordinates where the free surface can undergo severe deformations, including impact with solid or porous boundaries and impact between converging fluid fronts. The method is also capable of handling the breakup of a fluid front from the main body of fluid as well as their eventual coalescence. The technique has been validated by comparison with the results of tank experiments conducted at the University of Washington at Seattle (UW). In addition, collaboration with Urban Regional Research (URR) has lead to the modeling of specific scenarios that are representative of tsunami interactions with slender structures.
Significant progress has been made on the second and third goals by the development of a novel approach to define and track arbitrary, curvilinear surfaces by the use of Lagrangian boundary markers in a manner similar to the tracking of the free surface with surface markers. These latest advances have been demonstrated in two spatial dimensions, and must now be extended to three dimensions to be useful in tsunami mitigation. The extension to three-dimensional space is one of the objectives proposed herein.

Research Objectives

This project represents a continuation of a comprehensive research program to understand local tsunami effects on man-made and natural structures. The research is intended to place particular emphasis on understanding tsunami-structure interactions that can lead to effective measures for damage mitigation. It is important to point out in this regard that modeling the basic free surface dynamics of an incompressible fluid represents, in and of itself, a challenging CFD problem. The problem is further complicated greatly if wave breaking, multiple fluid bodies, and interactions with solid and porous structures are also present, as is the case in local tsunami dynamics. For the simulation of tsunami landfall and its interactions with coastline structures, a sophisticated computing procedure is required from the start, and methods with limited ranges of applicability cannot be of much use. In essence, the method of choice must:

• offer the versatility of a combined Lagrangian-Eulerian approach;
• be able to track the free surface and/or interface with a high degree of accuracy and flexibility;
• allow for the tracking of multiple fluid bodies subsequent to front breakup;
• provide the basic computational framework for the simultaneous tracking of suspended solid particles;
• be numerically robust in order to handle high flow velocities and, just as importantly, high fluid impact velocities with solid obstacles.

The proposed three-dimensional marker and micro cell method, developed at SMU under the existing cooperative NSF funding, conforms with the aforementioned requirements; indeed, the goal of the development of the method has been to address these capabilities. Examples highlighting the capabilities of the existing method will be presented in a subsequent section of this proposal along with selected validation results. The objectives of the current proposal are to extend the capabilities of the Eulerian-Lagrangian Marker and Micro Cell (ELMMC-3D) technique to:

1. Model realistic scenarios targeted at the development of mitigation schemes. It is important, for example, to determine the effects of the large beachfront structures on smaller dwellings behind them, including impact forces, moments, and inundation levels.

   To achieve this task, the codes will be parallelized to run on large, multi-processor systems.

2. Investigate the effects of tsunami forests, vegetation, and impact with other coastal obstacles such as breakwaters.

   To achieve this task, the method is being extended to handle porous media.

3. Investigate the transport of large solid obstacles by a tsunami wave.

   To achieve this task, the capability to represent curvilinear boundaries and arbitrarily moving objects within a Cartesian grid system is required. Preliminary developments have been made in two spatial dimensions and a proof of concept has been successfully completed.

4. Study the scouring effects behind blunt structures.

   To achieve this task, the fundamental ability to model large eddy turbulence will be required. The ELMMC-3D method is already capable of resolving all viscous effects down to the scale of the macro cell. However, smaller scale eddies will have to be modeled.

5. Introduce a Large-Eddy Simulation (LES) capability into the ELMMC-3D method to model turbulent behavior, which will be of significance in the study of scouring and other small-scale effects.

Significance and Motivation

Numerical simulations of three recent tsunamis in Irian Jaya, Papua New Guinea, and Peru have underscored the reality that prediction capabilities of tsunami phenomena are inadequate in two major areas, one in modeling the source mechanisms and two in modeling the coastal effects. While the initial tsunami condition at the source plays an essential role in determining the maximum runup heights along the coast-line, the inference of an accurate initial condition from given seismic parameters remains a formidable task. The difficulty is mainly attributable to the lack of measurements of seafloor deformations and fault displacements. Whereas seismologists and geologists continue to develop better models, immediate and near-future needs for tsunami hazard mitigation can be more effectively addressed by improving the capability to calculate coastal inundation for any prescribed initial condition. Consequently, proposed herein is a comprehensive and collaborative research program that is focused on the coastal effects of tsunamis, with the ultimate aim of mitigating tsunami hazards. To mitigate tsunami coastal hazards, the first priority is to improve the identification of the tsunami-inundation zone; i.e., the coastal zone at high tsunami risk. In Japan, to minimize the inundation area, tsunami seawalls (often more than 10-m high) have been constructed along the shoreline. In the US, such high walls are not considered a tenable approach to hazard reduction. NOAA has launched a comprehensive effort in the US to estimate potential inundation zones along the Western States, Alaska, and Hawaii (Cf. http://www.pmel.noaa.gov/tsunami/time/). Once inundation zones are defined, civil defense authorities can design evacuation routes as well as routes for search and rescue, while urban planners can develop priorities for such measures as relocation of critical and high-occupancy facilities. The next level of a mitigation strategy is loss reduction in lives and property within the tsunami inundation zones. Here, specific tsunami runup and flow patterns must be considered. Thus, the proposed work includes the determination of the tsunami-induced forces and an assessment of whether these forces are strong enough to destroy idealized structures. As tsunamis run up a beach, they often move large pieces of debris and other objects such as cars and poles. These objects become water-born projectiles that can impact and destroy structures along the paths of the tsunami. Many of these structures could withstand the tsunami attack had the water-born objects not impacted them. Therefore, an important engineering problem is the determination of tsunami induced forces, which will enable better design of structures on the waterfront and help guide the decision making process in issues of land use. For example, engineering analyses of the type proposed herein might suggest relocating parking lots, which are generators of potentially deadly debris, behind beachfront structures in the densely populated regions of Southern California. The proposed cooperative program aims at achieving the following global objectives:

• To understand the fundamental turbulence phenomena associated with tsunami runup and their effects on forces on structures and scouring.
• To improve the prediction capability of tsunami runup models by including more accurately the effects of dispersion and wave breaking.
• To achieve practical means of describing the complex runup flows within the context of their interactions with structures, trees, rocks, and vehicles, as well as with other typical, complex coastal features such as berms, dunes, earthen dikes (typical around tank installations), and river inlets.
• The fourth objective is to develop benchmark problems and their solutions for validating numerical methods and for determining the adequacy of different approximations to applications in tsunami hazard reduction.

The advancement of this proposed research will contribute to other tsunami mitigation endeavors such as the tsunami database, bathymetry and coastal-topography data management, hazard mapping, education, warning, planning, and the development of community-model activities.

Description of the ELMMC-3D Technique

The ELMMC-3D technique is capable of simulating incompressible fluid flow problems in Cartesian coordinates where the free surface can undergo severe deformations, including impact with solid or porous boundaries and impact between converging fluid fronts. The method is also capable of handling the breakup of a fluid front from the main body of fluid as well as their eventual coalescence. In the ELMMC-3D method, the free surface is tracked by the use of massless, "floating" Lagrangian markers, while the flow field is calculated in a fixed, Eulerian system discretized with rectangular computational cells. The primitive variables are defined on what is referred to as a "staggered grid," in which the velocity components are defined on the cell faces and the scalar variables (i.e., pressure, velocity divergence, temperature, concentration) are defined on the cell centers. The surface markers delineate the full and empty parts of the computational domain and thus make it possible to accordingly flag the cells as full, empty, or surface. Surface cells and their neighboring full cells are subdivided into smaller cells, named micro cells. These micro cells, in conjunction with the surface markers, make it possible to prescribe free surface boundary conditions right on the free surface as opposed to at the centers of surface cells. In addition, computations need be carried out only in those cells that are flagged as full or surface.