Model-reduced variational fluid simulation

We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar- and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains

Simulating liquids on dynamically warping grids

We introduce dynamically warping grids for adaptive liquid simulation. Our primary contributions are a strategy for dynamically deforming regular grids over the course of a simulation and a method for efficiently utilizing these deforming grids for liquid simulation. Prior work has shown that unstructured grids are very effective for adaptive fluid simulations. However, unstructured grids often lead to complicated implementations and a poor cache hit rate due to inconsistent memory access. Regular grids, on the other hand, provide a fast, fixed memory access pattern and straightforward implementation. Our method combines the advantages of both: we leverage the simplicity of regular grids while still achieving practical and controllable spatial adaptivity. We demonstrate that our method enables adaptive simulations that are fast, flexible, and robust to null-space issues. At the same time, our method is simple to implement and takes advantage of existing highly-tuned algorithms

Simulation of Fluid-Structure Interaction based on an Immersed-Solid Method

Takeo Kajishima and Shintaro Takeuchi, "Simulation of Fluid-Structure Interaction based on an Immersed-Solid Method", Journal of Mechanical Engineering and Sciences, Vol. 5, pp.555-561, UMP, 201

A full Eulerian finite difference approach for solving fluid-structure coupling problems

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.Comment: 38 pages, 27 figures, accepted for publication in J. Comput. Phy

GPU High-Performance Framework for PIC-like Simulation Methods Using the Vulkan® Explicit API

Within computational continuum mechanics there exists a large category of simulation methods which operate by tracking Lagrangian particles over an Eulerian background grid. These Lagrangian/Eulerian hybrid methods, descendants of the Particle-In-Cell method (PIC), have proven highly effective at simulating a broad range of materials and mechanics including fluids, solids, granular materials, and plasma. These methods remain an area of active research after several decades, and their applications can be found across scientific, engineering, and entertainment disciplines. This thesis presents a GPU driven PIC-like simulation framework created using the Vulkan® API. Vulkan is a cross-platform and open-standard explicit API for graphics and GPU compute programming. Compared to its predecessors, Vulkan offers lower overhead, support for host parallelism, and finer grain control over both device resources and scheduling. This thesis harnesses those advantages to create a programmable GPU compute pipeline backed by a Vulkan adaptation of the SPgrid data-structure and multi-buffered particle arrays. The CPU host system works asynchronously with the GPU to maximize utilization of both the host and device. The framework is demonstrated to be capable of supporting Particle-in-Cell like simulation methods, making it viable for GPU acceleration of many Lagrangian particle on Eulerian grid hybrid methods. This novel framework is the first of its kind to be created using Vulkan® and to take advantage of GPU sparse memory features for grid sparsity

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

AJK2011-04001 A FULL EULERIAN FINITE DIFFERENCE METHOD FOR HYPERELASTIC PARTICLES IN FLUID FLOWS

ABSTRACT A full Eulerian finite difference method has been developed for solving a dynamic interaction problem between Newtonian fluid and hyperelastic material. It facilitates to simulate certain classes of problems, such that an initial and neutral configuration of a multi-component geometry converted from voxel-based data is provided on a fixed Cartesian mesh. A solid volume fraction, which has been widely used for multiphase flow simulations, is applied to describing the multicomponent geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for incompressible hyperelastic materials. The present Eulerian approach is confirmed to well reproduce the material deformation in the lid-driven flow and the particle-particle interaction in the Couette flow computed by means of the finite element method. It is applied to a Poiseuille flow containing biconcave neo-Hookean particles. The deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. INTRODUCTION Numerical simulations of Fluid-Structure Interaction (FSI) problems would make it possible to predict the effect of a medical treatment and help one decide the treatment strategy in clinical practice. In particular, a blood flow simulation is expected to contribute to assisting the surgical planning of a cardiovascular disease and a brain aneurysm. Recently, there are growing expectations for its applications along with a progress in imaging and computational technologies. It is also expected to contribute to the field of life science, such as in the understanding of the very essence of life and the demonstration of pathological mechanisms. It is of great importance to develop numerical techniques suitable for the characteristics of body tissues, which are flexible and complicated in shape, when attempting to rationalize and to generalize the fluidstructure coupled analyses. The expectations include the further understandings of the micro/mesoscopic behavior of the flexibly deformable Red Blood Cells (RBCs) in plasma useful for evaluating the macroscopic blood rheology, and the thrombosis formation as aggregation of platelets, of which th