THE NUMERICAL MODELING OF LAVA DOME EVOLUTION AT VOLCÁN DE COLIMA USING VOF AND SPH METHODS

Lava flows from extrusive volcanic eruptions can have catastrophic consequences both for human life and the environment. Modeling such situations is an important scientific problem. The main driving forces in the evolution of the mentioned lava flows are gravitational forces, viscous friction forces on the surface of the spill, and the processes of crystallization of molten rocks into lava plateau, tubes, and domes. In this paper, the mathematical model of an extrusive volcanic eruption includes the Navier–Stokes equation, the incompressibility equation, the viscous phase transfer equation, as well as the corresponding initial and boundary conditions. Mathematical models of volcanic lava flows are considered and compared within the Euler (Volume Of Fluid – VOF) and Lagrange (Smooth Particle Hydrodynamic – SPH) formulations. ANSYS Fluent, OpenFOAM, and SPlisHSPlasH packages were used for computer simulation. Computer simulation algorithms for the problem are implemented in C++ language. Numerical modeling of the evolution of a real lava dome formed at the Colima volcano (Mexico) in February–March 2013 was carried out. For this experiment, information about the dynamics of lava dome growth, collected during the eruption, was used. It is shown how the computer simulation approach makes it possible to establish the dependence of the lava dome morphology on the rheology of a highly viscous fluid and the intensity of lava outflow. © 2022 Chinese Journal of Dermatology. All rights reserved

Variational Stokes: A Unified Pressure-viscosity Solver for Accurate Viscous 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 Larionov, E., Batty, C., & Bridson, R. (2017). Variational Stokes: A Unified Pressure-viscosity Solver for Accurate Viscous Liquids. ACM Trans. Graph., 36(4), 101:1–101:11. https://doi.org/10.1145/3072959.3073628We propose a novel unsteady Stokes solver for coupled viscous and pressure forces in grid-based liquid animation which yields greater accuracy and visual realism than previously achieved. Modern fluid simulators treat viscosity and pressure in separate solver stages, which reduces accuracy and yields incorrect free surface behavior. Our proposed implicit variational formulation of the Stokes problem leads to a symmetric positive definite linear system that gives properly coupled forces, provides unconditional stability, and treats difficult boundary conditions naturally through simple volume weights. Surface tension and moving solid boundaries are also easily incorporated. Qualitatively, we show that our method recovers the characteristic rope coiling instability of viscous liquids and preserves fine surface details, while previous grid-based schemes do not. Quantitatively, we demonstrate that our method is convergent through grid refinement studies on analytical problems in two dimensions. We conclude by offering practical guidelines for choosing an appropriate viscous solver, based on the scenario to be animated and the computational costs of different methods.Natural Sciences and Engineering Research Council of Canad

An Efficient Geometric Multigrid Solver for Viscous Liquids

We present an efficient geometric Multigrid solver for simulating viscous liquids based on the variational approach of Batty and Bridson [2008]. Although the governing equations for viscosity are elliptic, the strong coupling between different velocity components in the discrete stencils mandates the use of more exotic smoothing techniques to achieve textbook Multigrid efficiency. Our key contribution is the design of a novel box smoother involving small and sparse systems (at most 9 x 9 in 2D and 15 x 15 in 3D), which yields excellent convergence rates and performance improvements of 3.5x - 13.8x over a naïve Multigrid approach. We employ a hybrid approach by using a direct solver only inside the box smoother and keeping the remaining pipeline assembly-free, allowing our solver to efficiently accommodate more than 194 million degrees of freedom, while occupying a memory footprint of less than 16 GB. To reduce the computational overhead of using the box smoother, we precompute the Cholesky factorization of the subdomain system matrix for all interior degrees of freedom. We describe how the variational formulation, which requires volume weights computed at the centers of cells, edges, and faces, can be naturally accommodated in the Multigrid hierarchy to properly enforce boundary conditions. Our proposed Multigrid solver serves as an excellent preconditioner for Conjugate Gradients, outperforming existing state-of-the-art alternatives. We demonstrate the efficacy of our method on several high resolution examples of viscous liquid motion including two-way coupled interactions with rigid bodies.This work was supported in part by the Rutgers University start-up grant, the Ralph E. Powe Junior Faculty Enhancement Award, and the Natural Sciences and Engineering Research Council of Canada (RGPIN-04360-2014, CRDPJ-499952-2016)

Divergence-Free SPH for Incompressible and Viscous Fluids

In this paper we present a novel Smoothed Particle Hydrodynamics (SPH) method for the efficient and stable simulation of incompressible fluids. The most efficient SPH-based approaches enforce incompressibility either on position or velocity level. However, the continuity equation for incompressible flow demands to maintain a constant density and a divergence-free velocity field. We propose a combination of two novel implicit pressure solvers enforcing both a low volume compression as well as a divergence-free velocity field. While a compression-free fluid is essential for realistic physical behavior, a divergence-free velocity field drastically reduces the number of required solver iterations and increases the stability of the simulation significantly. Thanks to the improved stability, our method can handle larger time steps than previous approaches. This results in a substantial performance gain since the computationally expensive neighborhood search has to be performed less frequently. Moreover, we introduce a third optional implicit solver to simulate highly viscous fluids which seamlessly integrates into our solver framework. Our implicit viscosity solver produces realistic results while introducing almost no numerical damping. We demonstrate the efficiency, robustness and scalability of our method in a variety of complex simulations including scenarios with millions of turbulent particles or highly viscous materials

EFFICIENT PARTICLE-BASED VISCOUS FLUID SIMULATION WITH VIDEO-GUIDED REAL-TO-VIRTUAL PARAMETER TRANSFER

Viscous fluids, such as honey and molten chocolate, are common materials frequently seen in our daily life. These viscous fluids exhibit characteristic behaviors. Capturing and understanding such dynamics have been required for various applications. Although recent research made advances in simulating the viscous fluid dynamics, still many challenges are left to be addressed. In this dissertation, I present novel techniques to more efficiently and accurately simulate viscous fluid dynamics and propose a parameter identification framework to facilitate the tedious parameter tuning steps for viscous materials. In fluid simulation, enforcing the incompressibility robustly and efficiently is essential. One known challenge is how to set appropriate boundary conditions for free surfaces and solid boundaries. I propose a new boundary handling approach for an incompressible particle-based solver based on the connectivity analysis for simulation particles. Another challenge is that previously proposed techniques do not scale well. To address this, I propose a new multilevel particle-based solver which constructs the hierarchy of simulation particles. These techniques improve the robustness and efficiency achieving the nearly linear scaling unlike previous approaches. To simulate characteristic behaviors of viscous fluids, such as coiling and buckling phenomena and adhesion to other materials, it is necessary to develop a specialized solver. I propose a stable and efficient particle-based solver for simulating highly viscous fluids by using implicit integration with the full form of viscosity. To simulate more accurate interactions with solid objects, I propose a new two-way fluid-solid coupling method for viscous fluids via the unified minimization. These approaches also improve the robustness and efficiency while generating rotational and sticky behaviors of viscous fluids. One important challenge for the physically-based simulation is that it is not obvious how to choose appropriate material parameters to generate our desirable behaviors of simulated materials. I propose a parameter identification framework that helps to tune material parameters for viscous fluids with example video data captured from real world fluid phenomena. This framework identifies viscosity parameters for the real viscous fluids while estimating the hidden variables for the fluids, and enables the parameter transfer from the real world to virtual environment.Doctor of Philosoph

Droplets, splashes and sprays: highly detailed liquids in visual effects production.

An often misunderstood or under-appreciated feature of the visual effects pipeline is the sheer quantity of components and layers that go into a single shot, or even, single effect. Liquids, often combining waves, splashes, droplets and sprays, are a particular example of this. Whilst there has been a huge amount of research on liquid simulation in the last decade or so, little has been successful in reducing the number of layers or elements required to create a plausible final liquid effect. Furthermore, the finer-scale phenomena of droplets and sprays, often introduced in this layered approach and crucial for plausibility, are some of the least well catered-for in the existing toolkit. In lieu of adequate tooling, creation of these elements relies heavily on non-physical methods, bespoke setups and artistic ingenuity. This project explores physically-based methods for creating these phenomena, demonstrat- ing improved levels of detail and plausibility over existing non-physical approaches. These provide an alternative to existing workflows that are heavily reliant on artistic input, allowing artists to focus efforts on creative direction rather than trying to recreate physical plausibility. We explore various approaches to increasing the level of detail captured in physically-based liquid simulations, developing a collection of tools that improve existing workflows. First, we investigate the potential of a re-simulation approach to increasing artist iteration on fluid simulations using previous simulation data. Following this, a novel droplet interaction model for ballistic particle simulations is developed to introduce higher levels of detail in simulations of liquid droplets and sprays. This allows physically-plausible interactions between droplet particles to be modelled efficiently and helps to create realistic droplet and spray behaviours. Then, to maximise the quality of the results of these and other particle-based simulations, we develop a high quality particle surfacing algorithm to handle the varied nature of inputs common in production. Finally, we discuss the development of an expression language to manipulate point and volume data commonly used in creating these simulations, as well as elsewhere throughout visual effects. This research was driven directly by production requirements in partnership with a world- leading visual effects studio, DNEG. Projects have been developed to immediately integrate into production, using efficient, industry-standard, open technologies such as OpenVDB. It is shown that the toolkit for splashing liquids, even at fine-scales, can be improved by incorporating greater physical motivation further demonstrating the importance of physical simulation in visual effects and suggesting effects similarly reliant on artistic input (e.g. character/skin deformation) may benefit from increased physical correctness