The nonlinear and non-stationary nature of Navier-Stokes equations produces fluid flows that can be noticeably different in appearance with subtle changes. In this paper we introduce a method that can analyze the intrinsic multiscale features of flow fields from a decomposition point of view, by using the Hilbert-Huang transform method on 3D fluid simulation. We show how this method can provide insights to flow styles and help modulate the fluid simulation with its internal physical information. We provide easy-toimplement algorithms that can be integrated with standard grid-based fluid simulation methods, and demonstrate how this approach can modulate the flow field and guide the simulation with different flow styles. The modulation is straightforward and relates directly to the flow¡¯s visual effect, with moderate computational overhead.
Markus Ihmsen · Jens Cornelis · Barbara Solenthaler · Christopher J Horvath · Matthias Teschner. Implicit Incompressible SPH. 2014.
Lentine M, Zheng W, Fedkiw R, et al. A novel algorithm for incompressible flow using only a coarse grid projection[J]. international conference on computer graphics and interactive techniques, 2010, 29(4).
Zhu B, Yang X, Fan Y, et al. Creating and Preserving Vortical Details in SPH Fluid[J]. Computer Graphics Forum, 2010, 29(7): 2207-2214.
Chenfanfu Jiang · Craig Schroeder · Andrew Selle · Joseph Teran · Alexey Stomakhin. The affine particle-in-cell method. 2015.
Chang Y, Bao K, Zhu J, et al. A particle-based method for granular flow simulation[J]. Science in China Series F: Information Sciences, 2012, 55(5): 1062-1072.
Cornelis J, Ihmsen M, Peer A, et al. IISPH-FLIP for incompressible fluids[J]. Computer Graphics Forum, 2014, 33(2): 255-262.
Yusuke Tsuda · Yonghao Yue · Yoshinori Dobashi · Tomoyuki Nishita. Visual simulation of mixed-motion avalanches with interactions between snow layers. 2010.
Ren B, Yan X, Yang T, et al. Fast SPH simulation for gaseous fluids[J]. The Visual Computer, 2016, 32(4): 523-534.
Suntae Kim · Jeongmo Hong. Visual simulation of turbulent fluids using MLS interpolation profiles. 2013.
Shiguang Liu · Yixin Xu · Junyong Noh · Yiying Tong. Visual fluid animation via lifting wavelet transform: Fluid animation via lifting wavelet transform. 2014.
Gaseous fluids may move slowly, as smoke does, or at high speed, such as occurs with explosions. High-speed gas flow is always accompanied by low-speed gas flow, which produces rich visual details in the fluid motion. Realistic visualization involves a complex dynamic flow field with both low and high speed fluid behavior. In computer graphics, algorithms to simulate gaseous fluids address either the low speed case or the high speed case, but no algorithm handles both efficiently. With the aim of providing visually pleasing results, we present a hybrid algorithm that efficiently captures the essential physics of both low- and high-speed gaseous fluids. We model the low speed gaseous fluids by a grid approach and use a particle approach for the high speed gaseous fluids. In addition, we propose a physically sound method to connect the particle model to the grid model. By exploiting complementary strengths and avoiding weaknesses of the grid and particle approaches, we produce some animation examples and analyze their computational performance to demonstrate the effectiveness of the new hybrid method.
Surface flow phenomena, such as rain water flowing down a tree trunk and progressive water front in a shower room, are common in real life. However, compared with the 3D spatial fluid flow, these surface flow problems have been much less studied in the graphics community. To tackle this research gap, we present an efficient, robust and high-fidelity simulation approach based on the shallow-water equations. Specifically, the standard shallow-water flow model is extended to general triangle meshes with a feature-based bottom friction model, and a series of coherent mathematical formulations are derived to represent the full range of physical effects that are important for real-world surface flow phenomena. In addition, by achieving compatibility with existing 3D fluid simulators and by supporting physically realistic interactions with multiple fluids and solid surfaces, the new model is flexible and readily extensible for coupled phenomena. A wide range of simulation examples are presented to demonstrate the performance of the new approach.
This work extends existing multiphase-fluid SPH frameworks to cover solid phases, including deformable bodies and granular materials. In our extended multiphase SPH framework, the distribution and shapes of all phases, both fluids and solids, are uniformly represented by their volume fraction functions. The dynamics of the multiphase system is governed by conservation of mass and momentum within different phases. The behavior of individual phases and the interactions between them are represented by corresponding constitutive laws, which are functions of the volume fraction fields and the velocity fields. Our generalized multiphase SPH framework does not require separate equations for specific phases or tedious interface tracking. As the distribution, shape and motion of each phase is represented and resolved in the same way, the proposed approach is robust, efficient and easy to implement. Various simulation results are presented to demonstrate the capabilities of our new multiphase SPH framework, including deformable bodies, granular materials, interaction between multiple fluids and deformable solids, flow in porous media, and dissolution of deformable solids.
De Goes F, Wallez C, Huang J, et al. Power particles: an incompressible fluid solver based on power diagrams[J]. ACM Transactions on Graphics, 2015, 34(4).
Peer A, Ihmsen M, Cornelis J, et al. An implicit viscosity formulation for SPH fluids[J]. ACM Transactions on Graphics, 2015, 34(4).
Ando R, Thuerey N, Wojtan C, et al. A stream function solver for liquid simulations[J]. ACM Transactions on Graphics, 2015, 34(4).
Natsui S, Nashimoto R, Takai H, et al. SPH simulations of the behavior of the interface between two immiscible liquid stirred by the movement of a gas bubble[J]. Chemical Engineering Science, 2016: 342-355.
Takahashi T, Dobashi Y, Fujishiro I, et al. Implicit Formulation for SPH-based Viscous Fluids[J]. Computer Graphics Forum, 2015, 34(2): 493-502.
Ren B, Jiang Y, Li C, et al. A simple approach for bubble modelling from multiphase fluid simulation[J]. Computational Visual Media, 2015, 1(2): 171-181.
Tao Yang · Ming C Lin · Ralph R Martin · Jian Chang · Shimin Hu. Versatile interactions at interfaces for SPH-based simulations. 2016.
Tao Yang · Jian Chang · Bo Ren · Ming C Lin · Jian J Zhang · Shimin Hu. Fast multiple-fluid simulation using Helmholtz free energy. 2015.
T Weaver · Z Xiao. Fluid Simulation by the Smoothed Particle Hydrodynamics Method: A Survey. 2016.
Seungho Baek · Kiwon Um · Junghyun Han. Muddy water animation with different details: Muddy water animation with different details. 2015.
This paper presents a versatile and robust SPH simulation approach for multiple-fluid flows. The spatial distribution of different phases or components is modeled using the volume fraction representation, the dynamics of multiple-fluid flows is captured by using an improved mixture model, and a stable and accurate SPH formulation is rigorously derived to resolve the complex transport and transformation processes encountered in multiple-fluid flows. The new approach can capture a wide range of realworld multiple-fluid phenomena, including mixing/unmixing of miscible and immiscible fluids, diffusion effect and chemical reaction etc. Moreover, the new multiple-fluid SPH scheme can be readily integrated into existing state-of-the-art SPH simulators, and the multiple-fluid simulation is easy to set up. Various examples are presented to demonstrate the effectiveness of our approach.
In this paper, our aim is to present (1) an embedded fracture model (EFM) for coupled flow and mechanics problem based on the dual continuum approach on the fine grid and (2) an upscaled model for the resulting fine grid equations. The mathematical model is described by the coupled system of equation for displacement, fracture and matrix pressures. For a fine grid approximation, we use the finite volume method for flow problem and finite element method for mechanics. Due to the complexity of fractures, solutions have a variety of scales, and fine grid approximation results in a large discrete system. Our second focus in the construction of the upscaled coarse grid poroelasticity model for fractured media. Our upscaled approach is based on the nonlocal multicontinuum (NLMC) upscaling for coupled flow and mechanics problem, which involves computations of local basis functions via an energy minimization
In this paper, we present a novel pairwise-force smoothed particle hydrodynamics (PF-SPH) model to allow modeling of
various interactions at interfaces in real time. Realistic capture of interactions at interfaces is a challenging problem for SPH-based simulations, especially for scenarios involving multiple interactions at different interfaces. Our PF-SPH model can readily handle multiple kinds of interactions simultaneously in a single simulation; its basis is to use a larger support radius than that used in standard SPH. We adopt a novel anisotropic filtering term to further improve the performance of interaction forces. The proposed model is stable; furthermore, it avoids the particle clustering problem which commonly occurs at the free surface. We show how our model can be used to capture various interactions. We also consider the close connection between droplets and bubbles, and show how to animate bubbles rising in liquid as well as bubbles in air. Our method is versatile, physically plausible and easy-to-implement. Examples are provided to demonstrate the capabilities and effectiveness of our approach.
In this paper, we prove the global existence of solutions with analytic regularity to the 2D magnetohydrodynamic (MHD) boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multiscale expansion in [D. Gerard-Varet and M. Prestipino, <i>Z. Angew. Math. Phys.</i>, 68 (2017), 76]. The analysis shows that the combined effect of the magnetic diffusivity and transverse magnetic field on the boundary leads to a linear damping on the tangential velocity field near the boundary. And this damping effect yields the global-in-time analytic norm estimate in the tangential space variable on the perturbation of the classical steady Hartmann profile.
In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane with no-slip condition on the velocity field, perfectly conducting wall condition on the magnetic field and Dirichlet boundary condition on the temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer which is described by a Prandtl-type system. Under the non-degeneracy condition on the tangential magnetic field instead of monotonicity of velocity, by applying a coordinate transformation in terms of the stream function of magnetic field as motivated by the recent work , we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.
Myxobacteria are social bacteria, that can glide in two dimensions and form counterpropagating, interacting waves. Here, we present a novel age-structured, continuous macroscopic model for the movement of myxobacteria. The derivation is based on microscopic interaction rules that can be formulated as a particle-based model and set within the Self-Organized Hydrodynamics (SOH) framework. The strength of this combined approach is that microscopic knowledge or data can be incorporated easily into the particle model, whilst the continuous model allows for easy numerical analysis of the diﬀerent eﬀects. However, we found that the derived macroscopic model lacks a diﬀusion term in the density equations, which is necessary to control the number of waves, indicating that a higher order approximation during the derivation is crucial. Upon ad hoc addition of the diﬀusion term, we found very good agreement between the age-structured model and the biology. In particular, we analyzed the inﬂuence of a refractory (insensitivity) period following a reversal of movement. Our analysis reveals that the refractory period is not necessary for wave formation, but essential to wave synchronization, indicating separate molecular mechanisms.