Bingham fluid simulations using a physically consistent particle method

The Bingham fluid simulation model was constructed and validated using a physically consistent particle method, i.e., the Moving Particle Hydrodynamics (MPH) method. When a discrete particle system satisfies the fundamental laws of physics, the method is asserted as physically consistent. Since Bingham fluids sometimes show solid-like behaviors, linear and angular momentum conservation is especially important. These features are naturally satisfied in the MPH method. To model the Bingham feature, the viscosity of the fluid was varied to express the stress-strain rate relation. Since the solid-like part, where the stress does not exceed the yield stress, was modeled with very large viscosity, the implicit velocity calculation was introduced so as to avoid the restriction of the time step width with respect to the diffusion number. As a result, the present model could express the stopping and solid-like behaviors, which are characteristics of Bingham fluids. The proposed method was verified and validated, and its capability was demonstrated through calculations of the two-dimensional Poiseuille flow of a Bingham plastic fluid and the three-dimensional dam-break flow of a Bingham pseudoplastic fluid by comparing those computed results to theory and experiment

Conformation constraints for efficient viscoelastic fluid simulation

The simulation of high viscoelasticity poses important computational challenges. One is the difficulty to robustly measure strain and its derivatives in a medium without permanent structure. Another is the high stiffness of the governing differential equations. Solutions that tackle these challenges exist, but they are computationally slow. We propose a constraint-based model of viscoelasticity that enables efficient simulation of highly viscous and viscoelastic phenomena. Our model reformulates, in a constraint-based fashion, a constitutive model of viscoelasticity for polymeric fluids, which defines simple governing equations for a conformation tensor. The model can represent a diverse palette of materials, spanning elastoplastic, highly viscous, and inviscid liquid behaviors. In addition, we have designed a constrained dynamics solver that extends the position-based dynamics method to handle efficiently both position-based and velocity-based constraints. We show results that range from interactive simulation of viscoelastic effects to large-scale simulation of high viscosity with competitive performance

A Unified Particle-Based Solver for Non-Newtonian Behaviors Simulation

In this paper, we present a unified framework to simulate non-Newtonian behaviors. We combine viscous and elasto-plastic stress into a unified particle solver to achieve various non-Newtonian behaviors ranging from fluid-like to solid-like. Our constitutive model is based on a Generalized Maxwell model, which incorporates viscosity, elasticity and plasticity in one non-linear framework by a unified way. On the one hand, taking advantage of the viscous term, we construct a series of strain-rate dependent models for classical non-Newtonian behaviors such as shear-thickening, shear-thinning, Bingham plastic, etc. On the other hand, benefiting from the elasto-plastic model, we empower our framework with the ability to simulate solid-like non-Newtonian behaviors, i.e., visco-elasticity/plasticity. In addition, we enrich our method with a heat diffusion model to make our method flexible in simulating phase change. Through sufficient experiments, we demonstrate a wide range of non-Newtonian behaviors ranging from viscous fluid to deformable objects. We believe this non-Newtonian model will enhance the realism of physically-based animation, which has great potential for computer graphics.Comment: 12 page

High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.Comment: submitted to JNNFM Sept. 2020, revised March 202

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

Planning Framework for Robotic Pizza Dough Stretching with a Rolling Pin

Stretching a pizza dough with a rolling pin is a nonprehensile manipulation. Since the object is deformable, force closure cannot be established, and the manipulation is carried out in a nonprehensile way. The framework of this pizza dough stretching application that is explained in this chapter consists of four sub-procedures: (i) recognition of the pizza dough on a plate, (ii) planning the necessary steps to shape the pizza dough to the desired form, (iii) path generation for a rolling pin to execute the output of the pizza dough planner, and (iv) inverse kinematics for the bi-manual robot to grasp and control the rolling pin properly. Using the deformable object model described in Chap. 3, each sub-procedure of the proposed framework is explained sequentially

An adaptive variational finite difference framework for efficient symmetric octree viscosity

While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, while supporting viscous buckling and rotation effects, variable viscosity, and interaction with scripted moving solids. In experimental comparisons against regular grids, our method reduced the number of active velocity degrees of freedom by as much as a factor of 7.7 and reduced linear system solution times by factors between 3.8 and 9.4. We achieve this by developing a novel adaptive variational finite difference methodology for octrees and applying it to the optimization form of the viscosity problem. This yields a linear system that is symmetric positive definite by construction, unlike naive finite difference/volume methods, and much sparser than a hypothetical finite element alternative. Grid refinement studies show spatial convergence at first order in L∞ and second order in L1, while the significantly smaller size of the octree linear systems allows for the solution of viscous forces at higher effective resolutions than with regular grids. We demonstrate the practical benefits of our adaptive scheme by replacing the regular grid viscosity step of a commercial liquid simulator (Houdini) to yield large speed-ups, and by incorporating it into an existing inviscid octree simulator to add support for viscous flows. Animations of viscous liquids pouring, bending, stirring, buckling, and melting illustrate that our octree method offers significant computational gains and excellent visual consistency with its regular grid counterpart.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (RGPIN-04360-2014, CRDPJ-499952-2016) and the Rutgers University start-up grant

Particle-based fluids for viscous jet buckling

In this paper, we introduce a novel meshfree framework for animating free surface viscous liquids with\ud jet buckling effects, such as coiling and folding. Our method is based on Smoothed Particle Hydrodynamics\ud (SPH) fluids and allows more realistic and complex viscous behaviors than the previous SPH\ud frameworks in computer animation literature. The viscous liquid is modeled by a non-Newtonian fluid\ud flow and the variable viscosity under shear stress is achieved using a viscosity model known as Cross\ud model. We demonstrate the efficiency and stability of our framework in a wide variety of animations,\ud including scenarios with arbitrary geometries and high resolution of SPH particles. The interaction of the\ud viscous liquid with complex solid obstacles is performed using boundary particles. Our framework is\ud able to deal with different inlet velocity profiles and geometries of the injector, as well as moving inlet\ud jet along trajectories given by cubic Hermite splines. Moreover, the simulation speed is significantly\ud accelerated by using Computer Unified Device Architecture (CUDA) computing platform.FAPESP (Bolsas nº: 13/19760-5 e 14/09546-9)CNP