HyPAM [Zhang and Liu 2009 J. Comput. Phys. In press, doi:10.1016/j.jcp.2008.10.029] is a new hybrid continuum-particle framework developed by Qinghai Zhang. HyPAM addresses three major issues associated with numerical simulations of complex free-surface flows, viz. interface tracking, fragmentation and large physical jumps. HyPAM consists of three parts: (1) the Polygonal Area Mapping (PAM) method for interface tracking; (2) a new graph-based single-phase decomposition algorithm that decomposes a phase into a continuum zone, a buffer zone and a particle zone; (3) a 'passive-response' assumption, in which the air phase is assumed to respond passively to the continuum part of the water phase.
The PAM method [Zhang and Liu 2008 J. Comput. Phys. 227(8):4063-4088] represents material areas explicitly as piecewise polygons, traces characteristic points on polygon boundaries along pathlines and calculates new material areas inside interface cells via polygon-clippings in a discrete manner. PAM has very little spatial numerical diffusion and tracks the interface singularities naturally and accurately. In addition to its high accuracy, PAM can be directly used on either a structured rectangular mesh or an unstructured mesh without any modifications. The results from a set of widely used benchmark tests, e.g. the vortex test and deformation test, show that the PAM method is superior to existing volume-of-fluid (VOF) methods. In fact, it can be rigorously proven that VOF methods are not consistent while the PAM method is [Zhang and Liu 2008 SIAM J Numer. Anal., submitted].
For the illustration and validation of HyPAM, A number of examples, including water droplet impact, solitary wave propagation, and dam-break problems, are simulated. The hybrid feature of HyPAM can be clearly observed in a more detailed examination on spilling breakers in a dam-break test. It is shown that HyPAM is more accurate and versatile than Cobras. One major contribution of this work is the single-phase decomposition algorithm, useful for many other hybrid formulations.
Future improvements of HyPAM include the following:
incorporation of irregular solid boundaries into HyPAM; (work in progress) generalization of the PAM method to 3-D dimensions and for tracking interface of more than 2 materials; increasing the accuracy of Navier-Stokes solver to fourth-order accuracy; (work in progress) enlarging the application range of HyPAM by utilizing the Adaptive Mesh Refinement (AMR) technique. (Note: DivX codec is required to view the animations.)
COMCOT (Cornell Multi-grid Coupled Tsunami Model) is a tsunami modeling package, capable of simulating the entire lifespan of a tsunami, from its generation, propagation and runup/rundown on coastal regions.
COMCOT adopts leap-frog Finite Differencing Method to solve Shallow Water Equations in Spherical/Cartesian Coordinates. With the flexible nested grids setup, it can balance the accuracy and efficiency fairly well.
The model has been used to investigate several historical tsunami events, such as the 1960 Chilean tsunami, the 1992 Flores Islands (Indonesia) tsunami (Liu et al., 1994; Liu et al., 1995), the 2003 Algeria Tsunami (Wang and Liu, 2005) and more recently the 2004 Indian Ocean tsunami (Wang and Liu, 2006).
COBRAS (Cornell Breaking Waves and Structure) is a two-dimensional numerical model that solves the Reynolds Averaged Navier-Stokes Equations (RANS) for the mean flow field with a modified k-epsilon turbulence closure based on the nonlinear eddy viscosity assumption. The volume of fluid (VOF) method is employed to track the free surface movement. The model has been tested to be robust in the simulation of wave propagation in the surf zone, wave breaking and wave-structure interactions.
Recently, dynamic processes of bore propagation over a uniform slope are studied numerically using Cobras [Zhang and Liu 2008 Coast. Eng. doi:10.1016/j.coastaleng.2008.04.010]. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the 'mini-collapse' during the runup phase and the 'back-wash bore' in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged Turbulence Kinetic Energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate.
CoulWave (Cornell University Long and Intermediate Wave Modeling Package) was initially developed by Patrick J. Lynett and Philip L.-F. Liu. The governing equations employed in this numerical model allow for the evolution of fully nonlinear (wave amplitude to water depth ratio = O(1) ) and dispersive waves over variable bathymetry.
The numerical model uses a predictor-corrector scheme to march forward in time, and uses finite differences to approximate spatial derivatives. The model is formally accurate to fourth order both in time and in space.
More details can be found at the personal homepage of Professor Lynett at Texas A&M Univ. Click HERE to download technical document about CoulWave.