Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps

© ACM, 2016. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Azevedo, V. C., Batty, C., & Oliveira, M. M. (2016). Preserving Geometry and Topology for Fluid Flows with Thin Obstacles and Narrow Gaps. Acm Transactions on Graphics, 35(4), 97. https://doi.org/10.1145/2897824.292591Fluid animation methods based on Eulerian grids have long struggled to resolve flows involving narrow gaps and thin solid features. Past approaches have artificially inflated or voxelized boundaries, although this sacrifices the correct geometry and topology of the fluid domain and prevents flow through narrow regions. We present a boundary-respecting fluid simulator that overcomes these challenges. Our solution is to intersect the solid boundary geometry with the cells of a background regular grid to generate a topologically correct, boundary-conforming cut-cell mesh. We extend both pressure projection and velocity advection to support this enhanced grid structure. For pressure projection, we introduce a general graph-based scheme that properly preserves discrete incompressibility even in thin and topologically complex flow regions, while nevertheless yielding symmetric positive definite linear systems. For advection, we exploit polyhedral interpolation to improve the degree to which the flow conforms to irregular and possibly non-convex cell boundaries, and propose a modified PIC/FLIP advection scheme to eliminate the need to inaccurately reinitialize invalid cells that are swept over by moving boundaries. The method naturally extends the standard Eulerian fluid simulation framework, and while we focus on thin boundaries, our contributions are beneficial for volumetric solids as well. Our results demonstrate successful one-way fluid-solid coupling in the presence of thin objects and narrow flow regions even on very coarse grids.Conselho Nacional de Desenvolvimento Científico e Tecnológico, Natural Sciences and Engineering Research Council of Canad

Efficient Dynamic Unstructured Methods and Applications for Transonic Flows and Hypersonic Stage Separation

Relative-moving boundary problems have a wide variety of applications. They appear in staging during a launch process, store separation from a military aircraft, rotor-stator interaction in turbomachinery, and dynamic aeroelasticity. The dynamic unstructured technology (DUT) is potentially a strong approach to simulate unsteady flows around relative-moving bodies, by solving time-dependent governing equations. The dual-time stepping scheme is implemented to improve its efficiency while not compromising the accuracy of solutions. The validation of the implicit scheme is performed on a pitching NACA0012 airfoil and a rectangular wing with low reduced frequencies in transonic flows. All the matured accelerating techniques, including the implicit residual smoothing, the local time stepping, and the Full-Approximate-Scheme (FAS) multigrid method, are resorted once a dynamic problem is transformed into a series of “static” problems. Even with rather coarse Euler-type meshes, one order of CPU time savings is achieved without losing the accuracy of solutions in comparison to the popular Runge-Kutta scheme. More orders of CPU time savings are expected in real engineering applications where highly stretched viscous-type meshes are needed. The applicability of DUT is also extended from transonic/supersonic flows to hypersonic flows through special measures in spatial discretization to simulate the staging of a hypersonic vehicle. First, the simulations in Mach 5 and Mach 10 flights are performed on the longitudinal symmetry plane. A network of strong shocks and expansion waves are captured. A prescribed two-degrees-of-freedom motion is imposed on the booster and the adapter to mimic the staging. Then, a 3-D static Euler solver with an efficient edge-based data structure is modified for time-accurate flows. The overall history of aerodynamic interference during the staging in Mach 5 flight is obtained by an animation method, consisting of six static solutions along the assumed stage path. From the animation method, the following conclusions are made. After the booster and the adapter move away from the research vehicle by 60% vehicle length, their effects on the research vehicle are confined to the wake flow of the research vehicle. The aerodynamic forces on the research vehicle converge to the values in free flight when the booster is away from the research vehicle by 1.77 times vehicle length. The aerodynamic interference is a highly nonlinear function in terms of the distance between the vehicle, the booster, and the adapter. Finally, two dynamic computations are performed when the booster and the adapter are extremely close to the research vehicle. It is observed from these 3-D dynamic computations that as the stage separation advances, the aerodynamic interference becomes less sensitive to further relative motions

Arbitrary Lagrangian-Eulerian Method Investigation On Fuel Tank Strap Simulation Under Proving Ground Condition

The Arbitrary Lagrangian-Eulerian (ALE) is a hybrid finite element formulation that can alleviate many of the drawbacks from the traditional Lagrangian-based and Eulerian-based finite element simulations, which is developed through combining modern algorithms for Lagrangian hydrodynamics, meshing technology and remap methods developed for high-resolution Eulerian methods. Lagrangian-based finite element formulations is that the computational system moves with the material and main drawback is that it will face severe problems to deal with strong distortions in the computational domain. Eulerian-based finite element formulations is that the computational system is a prior fixed in space and unable to deal easily with fluids undergo large distortions at the interface. The use of Arbitrary Lagrangian-Eulerian (ALE) computer codes has been an enabling technology for many important applications. When using the ALE technique in engineering simulations, the computational mesh inside the domains can move arbitrarily to optimize the shapes of elements, while the mesh on the boundaries and interfaces of the domains can move along with materials to precisely track the boundaries and interfaces of a multi-material system. In automotive CAE durability analysis, simulation of dynamic stress and fatigue life of fuel tank straps is a complex problem. Typically a fuel tank is held with fuel tank straps. Its movement lies in the domain of nonlinear large rotation dynamics. Moreover, the sloshing behavior in the fuel tank makes the problem even more intricate. The objective of this study is to investigate the advantage of ALE method in simulating fuel sloshing through fuel tank and fuel tank strap movement under proving ground conditions using the nonlinear large rotation dynamic method with RADIOSS, a commercial code. After the stress distribution of the fuel tank strap is achieved, a commercial fatigue code, nCode DesignLife, is used to predict the fatigue life of the fuel tank straps. In this research, the stress distribution of the fuel tank strap can be predicted with Arbitrary Lagrangian-Eulerian Method (ALE) to simulate fuel sloshing which plays critical role in fuel mass redistribution and the stress variation with time. A commercial fatigue code, nCode DesignLife, is used to predict the fatigue life of the fuel tank straps. The analyses have accurately predicted the crack initiation location and sequence in the fuel tank straps, and show good correlation with test. The utilization of this method can give design direction to minimize the iteration of lab testing and expedite the design period

Controlling the Error on Target Motion through Real-time Mesh Adaptation: Applications to Deep Brain Stimulation

We present an error-controlled mesh refinement procedure for needle insertion simulation and apply it to the simulation of electrode implantation for deep brain stimulation, including brain shift. Our approach enables to control the error in the computation of the displacement and stress fields around the needle tip and needle shaft by suitably refining the mesh, whilst maintaining a coarser mesh in other parts of the domain. We demonstrate through academic and practical examples that our approach increases the accuracy of the displacement and stress fields around the needle without increasing the computational expense. This enables real-time simulations. The proposed methodology has direct implications to increase the accuracy and control the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anesthesia, or cryotherapy and can be essential to the development of robotic guidance.Comment: 21 pages, 14 figure

Adaptive Physically Based Models in Computer Graphics

International audienceOne of the major challenges in physically-based modeling is making simulations efficient. Adaptive models provide an essential solution to these efficiency goals. These models are able to self-adapt in space and time, attempting to provide the best possible compromise between accuracy and speed. This survey reviews the adaptive solutions proposed so far in computer graphics. Models are classified according to the strategy they use for adaptation, from time-stepping and freezing techniques to geometric adaptivity in the form of structured grids, meshes, and particles. Applications range from fluids, through deformable bodies, to articulated solids

Liquid simulation with mesh-based surface tracking

Animating detailed liquid surfaces has always been a challenge for computer graphics researchers and visual effects artists. Over the past few years, researchers in this field have focused on mesh-based surface tracking to synthesize extremely detailed liquid surfaces as efficiently as possible. This course provides a solid understanding of the steps required to create a fluid simulator with a mesh-based liquid surface. The course begins with an overview of several existing liquid-surface-tracking techniques and the pros and cons of each method. Then it explains how to embed a triangle mesh into a finite-difference-based fluid simulator and describes several methods for allowing the liquid surface to merge together or break apart. The final section showcases the benefits and further applications of a mesh-based liquid surface, highlighting state-of-the-art methods for tracking colors and textures, maintaining liquid volume, preserving small surface features, and simulating realistic surface-tension waves

Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids

© ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Aanjaneya, M., Gao, M., Liu, H., Batty, C., & Sifakis, E. (2017). Power Diagrams and Sparse Paged Grids for High Resolution Adaptive Liquids. ACM Trans. Graph., 36(4), 140:1–140:12. https://doi.org/10.1145/3072959.3073625We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancements to adaptive level set advection, velocity extrapolation, and the fast marching method for redistancing. Our overall framework gracefully accommodates the task of dynamically adapting the octree topology during simulation. We demonstrate end-to-end simulations of complex adaptive flows in irregularly shaped domains, with tens of millions of degrees of freedom.National Science FoundationNational Sciences and Engineering Research Council of Canad

IST Austria Thesis

Computer graphics is an extremely exciting field for two reasons. On the one hand, there is a healthy injection of pragmatism coming from the visual effects industry that want robust algorithms that work so they can produce results at an increasingly frantic pace. On the other hand, they must always try to push the envelope and achieve the impossible to wow their audiences in the next blockbuster, which means that the industry has not succumb to conservatism, and there is plenty of room to try out new and crazy ideas if there is a chance that it will pan into something useful. Water simulation has been in visual effects for decades, however it still remains extremely challenging because of its high computational cost and difficult artdirectability. The work in this thesis tries to address some of these difficulties. Specifically, we make the following three novel contributions to the state-of-the-art in water simulation for visual effects. First, we develop the first algorithm that can convert any sequence of closed surfaces in time into a moving triangle mesh. State-of-the-art methods at the time could only handle surfaces with fixed connectivity, but we are the first to be able to handle surfaces that merge and split apart. This is important for water simulation practitioners, because it allows them to convert splashy water surfaces extracted from particles or simulated using grid-based level sets into triangle meshes that can be either textured and enhanced with extra surface dynamics as a post-process. We also apply our algorithm to other phenomena that merge and split apart, such as morphs and noisy reconstructions of human performances. Second, we formulate a surface-based energy that measures the deviation of a water surface froma physically valid state. Such discrepancies arise when there is a mismatch in the degrees of freedom between the water surface and the underlying physics solver. This commonly happens when practitioners use a moving triangle mesh with a grid-based physics solver, or when high-resolution grid-based surfaces are combined with low-resolution physics. Following the direction of steepest descent on our surface-based energy, we can either smooth these artifacts or turn them into high-resolution waves by interpreting the energy as a physical potential. Third, we extend state-of-the-art techniques in non-reflecting boundaries to handle spatially and time-varying background flows. This allows a novel new workflow where practitioners can re-simulate part of an existing simulation, such as removing a solid obstacle, adding a new splash or locally changing the resolution. Such changes can easily lead to new waves in the re-simulated region that would reflect off of the new simulation boundary, effectively ruining the illusion of a seamless simulation boundary between the existing and new simulations. Our non-reflecting boundaries makes sure that such waves are absorbed

Learning Space-Time Continuous Neural PDEs from Partially Observed States

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an efficient probabilistic framework and a novel encoder design for improved data efficiency and grid independence. The latent state dynamics are governed by a PDE model that combines the collocation method and the method of lines. We employ amortized variational inference for approximate posterior estimation and utilize a multiple shooting technique for enhanced training speed and stability. Our model demonstrates state-of-the-art performance on complex synthetic and real-world datasets, overcoming limitations of previous approaches and effectively handling partially-observed data. The proposed model outperforms recent methods, showing its potential to advance data-driven PDE modeling and enabling robust, grid-independent modeling of complex partially-observed dynamic processes