The GeoClaw software for depth-averaged flows with adaptive refinement

Many geophysical flow or wave propagation problems can be modeled with two-dimensional depth-averaged equations, of which the shallow water equations are the simplest example. We describe the GeoClaw software that has been designed to solve problems of this nature, consisting of open source Fortran programs together with Python tools for the user interface and flow visualization. This software uses high-resolution shock-capturing finite volume methods on logically rectangular grids, including latitude--longitude grids on the sphere. Dry states are handled automatically to model inundation. The code incorporates adaptive mesh refinement to allow the efficient solution of large-scale geophysical problems. Examples are given illustrating its use for modeling tsunamis, dam break problems, and storm surge. Documentation and download information is available at www.clawpack.org/geoclawComment: 18 pages, 11 figures, Animations and source code for some examples at http://www.clawpack.org/links/awr10 Significantly modified from original posting to incorporate suggestions of referee

Grid models versus TIN : geometric accuracy of multibeam data processing

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3D cut-cell modelling for high-resolution atmospheric simulations

Owing to the recent, rapid development of computer technology, the resolution of atmospheric numerical models has increased substantially. With the use of next-generation supercomputers, atmospheric simulations using horizontal grid intervals of O(100) m or less will gain popularity. At such high resolution more of the steep gradients in mountainous terrain will be resolved, which may result in large truncation errors in those models using terrain-following coordinates. In this study, a new 3D Cartesian coordinate non-hydrostatic atmospheric model is developed. A cut-cell representation of topography based on finite-volume discretization is combined with a cell-merging approach, in which small cut-cells are merged with neighboring cells either vertically or horizontally. In addition, a block-structured mesh-refinement technique is introduced to achieve a variable resolution on the model grid with the finest resolution occurring close to the terrain surface. The model successfully reproduces a flow over a 3D bell-shaped hill that shows a good agreement with the flow predicted by the linear theory. The ability of the model to simulate flows over steep terrain is demonstrated using a hemisphere-shaped hill where the maximum slope angle is resolved at 71 degrees. The advantage of a locally refined grid around a 3D hill, with cut-cells at the terrain surface, is also demonstrated using the hemisphere-shaped hill. The model reproduces smooth mountain waves propagating over varying grid resolution without introducing large errors associated with the change of mesh resolution. At the same time, the model shows a good scalability on a locally refined grid with the use of OpenMP.Comment: 19 pages, 16 figures. Revised version, accepted for publication in QJRM

Adaptive Methods for Point Cloud and Mesh Processing

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data. The major contributions of this research lie in four aspects: 1) Four order statistic algorithms are extended, and one adaptive filtering method is proposed for the noisy point cloud with improved results such as preserving significant features. These methods are applied to standard models as well as synthetic models, and real scenes, 2) A hardware acceleration of the proposed method using Microsoft parallel pattern library for filtering point clouds is implemented using multicore processors, 3) A new method for aerial LIDAR data filtering is proposed. The objective is to develop a method to enable automatic extraction of ground points from aerial LIDAR data with minimal human intervention, and 4) A novel method for mesh color sharpening using the discrete Laplace-Beltrami operator is proposed. Median and order statistics-based filters are widely used in signal processing and image processing because they can easily remove outlier noise and preserve important features. This dissertation demonstrates a wide range of results with median filter, vector median filter, fuzzy vector median filter, adaptive mean, adaptive median, and adaptive vector median filter on point cloud data. The experiments show that large-scale noise is removed while preserving important features of the point cloud with reasonable computation time. Quantitative criteria (e.g., complexity, Hausdorff distance, and the root mean squared error (RMSE)), as well as qualitative criteria (e.g., the perceived visual quality of the processed point cloud), are employed to assess the performance of the filters in various cases corrupted by different noisy models. The adaptive vector median is further optimized for denoising or ground filtering aerial LIDAR data point cloud. The adaptive vector median is also accelerated on multi-core CPUs using Microsoft Parallel Patterns Library. In addition, this dissertation presents a new method for mesh color sharpening using the discrete Laplace-Beltrami operator, which is an approximation of second order derivatives on irregular 3D meshes. The one-ring neighborhood is utilized to compute the Laplace-Beltrami operator. The color for each vertex is updated by adding the Laplace-Beltrami operator of the vertex color weighted by a factor to its original value. Different discretizations of the Laplace-Beltrami operator have been proposed for geometrical processing of 3D meshes. This work utilizes several discretizations of the Laplace-Beltrami operator for sharpening 3D mesh colors and compares their performance. Experimental results demonstrated the effectiveness of the proposed algorithms

Progressive refinement rendering of implicit surfaces

The visualisation of implicit surfaces can be an inefficient task when such surfaces are complex and highly detailed. Visualising a surface by first converting it to a polygon mesh may lead to an excessive polygon count. Visualising a surface by direct ray casting is often a slow procedure. In this paper we present a progressive refinement renderer for implicit surfaces that are Lipschitz continuous. The renderer first displays a low resolution estimate of what the final image is going to be and, as the computation progresses, increases the quality of this estimate at an interactive frame rate. This renderer provides a quick previewing facility that significantly reduces the design cycle of a new and complex implicit surface. The renderer is also capable of completing an image faster than a conventional implicit surface rendering algorithm based on ray casting