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OzViz 2009 Visualisation of Groundwater Flow using Texture Based Visualisation Techniques. David Warne (HPC and Research Support, QUT), Joe Young (HPC and Research Support, QUT), Ben Cumming (School of Mathematical Sciences, QUT)

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Background: Geological and/or human influences (such as over- extraction of ground water in dry seasons), can lead to lowering of pressure or lowering of the water table. [1] For a coastal aquifer, this can allow intrusion of salt water into the aquifer. As a result crops begin to get watered with highly saline water, and before long the soil can become useless. [1] Image Downloaded From: http://web.arc.losrios.edu/~borougt/SaltWaterIncursion.gif

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Background (cont...): Prediction of these flows requires mathematical simulations [2]. Complexity of flows. Long time periods involved. Handling variable soil saturation adds another level of complexity [3]. Numerically solved using schemes such as Finite Elements, or Finite Volumes [2][3][4].

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Project Overview: Project was initiated by Researchers at the School of Mathematical Sciences (QUT), to improve visualisation of simulation outputs. Visualisation is a fundamental step in furthering our understanding of these simulation outputs [5]. The following Visualisation goals were decided on with this in mind: Generate visualisation with rich flow information. Effectively related groundwater flow to the aquifer's variable properties that drive the flow. Identify regions of high and low flow. Enable the use of virtual dye experimentation.

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Data to Visualise: The data source comes from a numerical simulation program developed by researchers at the School of Mathematical Sciences at QUT. Simulates the physics of the groundwater flow problem, by solving a non-linear system of PDE's (using finite volumes). Uses an unstructured mesh to perform its computation. Represents a 2D cross section.

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Data to Visualise (cont...): The simulation code solves for the following variables at the node points. Pressure and pressure head of the water (you can think of pressure head as scaled by the fluids specific weight). Saturation (amount of water in the void space of the soil, expressed as a ratio). Salt Concentration (ranges from 0 to 1, 1 = salt water and 0 = fresh water). These values can then be used to derive the flow of the water and salt at the face centres.

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Visualisation of Flow Data: Prior to this project, visualisation of model output had not been effective. Two images needed to be generated (one for scalar properties and on for the flow field). Glyph plot for the flow field is very cluttered and difficult to see any detail. These fields are unsteady, so there is an evolution over time. The Glyph plots do not represent this well.

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Visualisation of Flow Data Great Improvements can be made using texture based methods. These techniques use random noise images, which are advected or warped by the underlying vector field. Two Algorithms where implemented: Image Based Flow Visualisation [5]. Lagrangian-Eulerian Advection [6]. Implemented in C/C++ with OpenGL for the Graphics.

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Image Based Flow Visualisation: Lets start off with a few movies.

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Image Based Flow Visualisation (cont...): The Algorithm: Start with mesh with a vector defined at each vertex. Warp the mesh based on the flow at time the current time slice. Map the previous frame to the warped mesh. Blend in a new noise image. Display this new image.

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Image Based Flow Visualisation (cont...):

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Advantages to IBFV: Works on unstructured meshes (even ones using arbitrary polygons). Naturally translates into OpenGL function calls an therefore the power of the GPU is easily harnessed [5],[7]. 8303 vertices with 512x512 texture images, rendering at 47 fps. (GeForce 9800GT)

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Lagrangian-Eularian Advection: Again We'll start off with a movie.

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Lagrangian-Eularian Advection (cont...): The Algorithm Initialise a WxH noise image. Integrate each particle backward in time. Advect the previous noise image to the new one. Store the new noise image for edge treatment and new noise injection. Blend the noise image with the previously displayed image. Post processing of frames.

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Lagrangian-Eularian Advection (cont...): The major component to the Algorithm is the Backwards integration of the particle coordinates. Backward integration removes holes forming.

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Lagrangian-Eularian Advection (cont...): Noise Injection: A percentage of pixels are selected at random to flip there intensities. This is to prevent spreading in regions of divergence. Edges need to be handled To achieve this a buffer zone of width h is include. New noise patterns are injected at each iteration to ensure particles flow into the field. Without this step streaks begin to form in the intake boundaries. Maximum advection displacement is set to h to avoid out of bounds indexing.

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Lagrangian-Eularian Advection (cont...): Advantages: Flow of particles, much clearer than IBFV. High Spatial and temporal Correlation of flow. Disadvantages: Designed for a regular mesh, so some interpolation may be needed (A cubic interpolation scheme was used for this specific case). More consideration needs to be made regarding high divergence, low velocities, and boundaries [6]. Not as easy to implement on the GPU (though definitely possible).

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Summary of Texture Based Methods Both IBFV and LEA are very effective techniques in visualisation of unsteady flow. Visual cues caused by the advection of textures, immediately give a sense of fluid flowing. Dense textures allow representation of the entire flow field, as opposed to a select number of pathlines (as is traditional [8],[9])

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Visualisation of Aquifer Variables: A goal of this project was to be able to correlate aquifer/fluid variables to the flow itself. Colour and opacity maps have been utilised here to achieve this goal.

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Density driven flow: A blue-white colour map has been blended with the underlying IBFV algorithm. The colourmap was selected since it is isomorphic, but also has the visual cues of blue for water and white for salt. The animations show clearly the denser salt water is the major driver the flow.

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Variable Saturation: A hypothetical scenario with two inlets (could be pumps), intruding on a completely unsaturated soil. Flow is driven by the pressure head, which is cased by the difference in soil saturation. Colour maps here Blue-white-Red for pressure head, and Blue-Brown for Saturation. Note that a pressure head of 0, corresponds to the soil becomes fully saturated. When the two water fronts meet the flow achieves a steady state.

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Identification of regions of Low/High flow. Location of high and low velocities can reveal more information about the flow. Location of Currents Location of regions of independent flow. Velocity masking was applied to the LEA algorithm to achieve this goal. Velocity masking can be achieved by mapping velocity to an opacity.

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Virtual Dye Experiments: Flow experimentation has often been performed through the use of injecting dye into the fluid, and tracing the advection of the dye [2]. Simulation of these dye experiments aid in exploration of simulation data [5],[6],[10]. IBFV and LEA can naturally be extended to perform dye advection (though there are some problems with these techniques [10]).

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Conclusions: Dense texture based methods are very effective techniques for visualisation of a flow field as a whole (full spatial coverage) [10]. Ground water flow systems are in need of improvements in the methods used for visualisation. The combination of texture based methods with colourmaps and velocity masks have produced a useful tool to aid research in this area. The addition of virtual dye experiments ideally allow the researcher to explore specific paths of individual or groups of particles [5],[6]. These trajectories are most likely a bit too simplistic for the physics of the systems behind them, but are still useful to view direction of flow.

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References: 1.M. L. Calvache and A. Pulido-Bosch. “Effects of geology and human activity on the dynamics of salt-water intrusion in three coastal aquifers in southern Spain”. Environmental Geolog. Vol. 30, no. 3-4, pp. 215-223, Apr. 1997. 2.A. Younes, PH. Ackerer, and R. Mose. “Modeling Variable Density Flow and Solute Transport in Porous Medium: 2. Re-Evaluation of the Sal Dome Flow Problem”. Transport in Porous Media, no. 35, pp. 375-394, 1999. 3. D. McBride, M.Cross, N. Croft, C. Bennet and J. Gebhardt. “Computational Modelling of Variably Saturated Flow in Porous Media with Three-Dimensional Geometries”. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, no. 50, pp. 1085- 1117, 2005 4.H.-J. G. Diersch and O. Koldite. “Variable-Density Flow and Transport in Porous Media: Approaches and Challenges”. Advances in Water Resources, no. 25, pp. 899-944, 2002. 5. J. J. Van Wijk. “Image Based Flow Visualization”. SIGGRAPH 2002 Conference Proceedings, pp.745-754, 2002. 6. B. Jobard, G. Eriebacher, and M. Y. Hussaini. “Lagrangian-Eulerian Advection of Noise and Dye Textures of Unsteady Flow Visualization”. IEEE Transactions on Visualization and Computer Graphics, vol. 8, no. 3, pp. 211-221, Jul. 2002. 7. A. C. Telea. “Data Visualization: Principles and Practice”. A K Peters Ltd, 2008. 8.D. A. Lane, “UFAT—A Particle Tracer for Time-Dependent Flow Fields”, Proc. IEEE Visualization '94, R. D. Bergeron and A. E. Kaufman, eds., pp. 257-264, 1994. 9.D. A. Lane, “Visualizing Time-Varying Phenomena in Numerical Simulations of Unsteady Flows ”, NASA Ames Research Center, Feb. 1996. 10. R. S. Laramee, H. Hauser, H. Doleisch, B. Vrolijk, F. H. Post, and D. Weiskopf. “The State of the Art in Flow Visualization: Dense and Texture-Based Techniques”, COMPUTER GRAPHICS forum, vol. 23, no. 2, pp. 203-221, 2004.

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