Diagnostic tools for 3D unstructured oceanographic data

Most ocean models in current use are built upon structured meshes. It follows that most existing tools for extracting diagnostic quantities (volume and surface integrals, for example) from ocean model output are constructed using techniques and software tools which assume structured meshes. The greater complexity inherent in unstructured meshes (especially fully unstructured grids which are unstructured in the vertical as well as the horizontal direction) has left some oceanographers, accustomed to traditional methods, unclear on how to calculate diagnostics on these meshes. In this paper we show that tools for extracting diagnostic data from the new generation of unstructured ocean models can be constructed with relative ease using open source software. Higher level languages such as Python, in conjunction with packages such as NumPy, SciPy, VTK and MayaVi, provide many of the high-level primitives needed to perform 3D visualisation and evaluate diagnostic quantities, e.g. density fluxes. We demonstrate this in the particular case of calculating flux of vector fields through isosurfaces, using flow data obtained from the unstructured mesh finite element ocean code ICOM, however this tool can be applied to model output from any unstructured grid ocean code

Multi-stage high order semi-Lagrangian schemes for incompressible flows in Cartesian geometries

Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy then determines the properties of the scheme. We introduce a simple multi-stage procedure which can easily be used to increase the order of accuracy of a code based on multi-linear interpolations. This approach is an extension of a corrective algorithm introduced by Dupont \& Liu (2003, 2007). This multi-stage procedure can be easily implemented in existing parallel codes using a domain decomposition strategy, as the communications pattern is identical to that of the multi-linear scheme. We show how a combination of a forward and backward error correction can provide a third-order accurate scheme, thus significantly reducing diffusive effects while retaining a non-dispersive leading error term.Comment: 14 pages, 10 figure

Image Space Tensor Field Visualization Using a LIC-like Method

Tensors are of great interest to many applications in engineering and in medical imaging, but a proper analysis and visualization remains challenging. Physics-based visualization of tensor fields has proven to show the main features of symmetric second-order tensor fields, while still displaying the most important information of the data, namely the main directions in medical diffusion tensor data using texture and additional attributes using color-coding, in a continuous representation. Nevertheless, its application and usability remains limited due to its computational expensive and sensitive nature. We introduce a novel approach to compute a fabric-like texture pattern from tensor fields on arbitrary non-selfintersecting surfaces that is motivated by image space line integral convolution (LIC). Our main focus lies on regaining three-dimensionality of the data under user interaction, such as rotation and scaling. We employ a multi-pass rendering approach to estimate proper modification of the LIC noise input texture to support the three-dimensional perception during user interactions

Evolving time surfaces and tracking mixing indicators for flow visualization

The complexity of large scale computational fluid dynamic simulations (CFD) demands powerful tools to investigate the numerical results. To analyze and understand these voluminous results, we need to visualize the 3D flow field. We chose to use a visualization technique called Time Surfaces. A time surface is a set of surfaces swept by an initial seed surface for a given number of timesteps. We use a front tracking approach where the points of an in initial surface are advanced in a Lagrangian fashion. To maintain a smooth time surface, our method requires surface refinement operations that either split triangle edges, adjust narrow triangles, or delete small triangles. In the conventional approach of edge splitting, we compute the length of an edge, and split that edge if it has exceeded a certain threshold length. In our new approach, we examine the angle between the two vectors at a given edge. We split the edge if the vectors are diverging from one another. This vector angle criterion enables us to refine an edge before advancing the surface front. Refining a surface prior to advancing it has the effect of minimizing the amount of interpolation error. In addition, unlike the edge length criterion which yields a triangular mesh with even vertex distribution throughout the surface, the vector angle criterion yields a triangular mesh that has fewer vertices where the vector field is flat and more vertices where the vector field is curved. Motivated by the evaluation and the analysis of flow field mixing quantities, this work explores two types of quantitative measurements. First, we look at Ottino\u27s mixing indicators which measure the degree of mixing of a fluid by quantifying the rate at which a sample fluid blob stretches in a flow field over a period of time. Using the geometry of the time surfaces we generated, we are able to easily evaluate otherwise complicated mixing quantities. Second, we compute the curvature and torsion of the velocity field itself. Visualizing the distribution and intensity of the curvature and torsion scalar fields enables us to identify regions of strong and low mixing. To better observe these scalar fields, we designed a multi-scale colormap that emphasizes small, medium, and large values, simultaneously. We test our time surface method and analyze fluid flow mixing quantities on two CFD datasets: a stirred tank simulation and a BP oil spill simulation

A scalar imaging velocimetry technique for fully resolved four‐dimensional vector velocity field measurements in turbulent flows

This paper presents an experimental technique for obtaining fully resolved measurements of the vector velocity field u(x,t) throughout a four‐dimensional spatiotemporal region in a turbulent flow. The method uses fully resolved four‐dimensional scalar field imaging measurements in turbulent flows [Phys. Fluids A 3, 1115 (1991)] to extract the underlying velocity field from the exact conserved scalar transport equation. A procedure for accomplishing this is described, and results from a series of test cases are presented. These involve synthetically generated scalar fields as well as actual measured turbulent flow scalar fields advected numerically by various imposed flow fields. The imposed velocity fields are exactly known, allowing a careful validation of the technique and its potential accuracy. Results obtained from a zeroth iteration of the technique are found to be very close to the exact underlying vector velocity field. Further results show that successive iterations bring the velocity field from the zeroth iteration even closer to the exact result. It is also shown that the comparatively dense velocity field information that this technique provides is well suited for accurate extraction of the more dynamically insightful strain rate and vorticity fields ϵ(x,t) and ω(x,t).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69930/2/PFADEB-4-10-2191-1.pd

A Vortex Method for Bi-phasic Fluids Interacting with Rigid Bodies

We present an accurate Lagrangian method based on vortex particles, level-sets, and immersed boundary methods, for animating the interplay between two fluids and rigid solids. We show that a vortex method is a good choice for simulating bi-phase flow, such as liquid and gas, with a good level of realism. Vortex particles are localized at the interfaces between the two fluids and within the regions of high turbulence. We gain local precision and efficiency from the stable advection permitted by the vorticity formulation. Moreover, our numerical method straightforwardly solves the two-way coupling problem between the fluids and animated rigid solids. This new approach is validated through numerical comparisons with reference experiments from the computational fluid community. We also show that the visually appealing results obtained in the CG community can be reproduced with increased efficiency and an easier implementation