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.
We analyze the power spectra and structure functions (SFs) of the temperature and radial velocity fields, calculated in the radial and azimuthal directions, in annular centrifugal Rayleigh–Bénard convection (ACRBC) for Rayleigh number Ra ∈[108,1011], Prandtl number Pr = 10.7, and inverse Rossby number Ro−1=16 using the spatial data obtained by quasi-two-dimensional direct numerical simulation. Bolgiano and Obukhov-like (BO59-like) scalings for the energy spectrum in both the azimuthal and radial directions and thermal spectrum in the azimuthal direction are observed. The range of BO59-like scaling becomes wider as Ra increases. At Ra=1011, it is found that BO59-like scaling Eu(kr)∼kr−11/5 spans nearly two decades for the energy spectrum calculated in the radial direction. Power-law fittings in the range larger than the Bolgiano scales, the scaling exponents of transverse and longitudinal velocity SFs vs the order coincide with the theoretical prediction of BO59 scaling ζ u p =3p/5 basically. The second-order temperature SFs exhibit a gradual transition from the Obukhov–Corrsin behavior at scales smaller than the Bolgiano scales to the BO59 behavior at scales larger than the Bolgiano scales. The slopes from the third to sixth-order temperature SFs are similar, which is similar to classical Rayleigh–Bénard convection and Rayleigh–Taylor turbulence. The probability density functions (p.d.f.) of temperature fluctuations δT/σT reveal the cold plumes are strong and the p.d.f. in different regions at high Ra are similar. The stronger turbulent-mixing and larger centrifugal buoyancy in ACRBC may result in the BO59-like scaling.
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.
Based on the fully compressible Navier-Stokes equations, the linear stability of thermal convection in rapidly rotating spherical shells of various radius ratios eta is studied for a wide range of Taylor number Ta, Prandtl number Pr and the number of density scale height N-rho. Besides the classical inertial mode and columnar mode, which are widely studied by the Boussinesq approximation and anelastic approximation, the quasi-geostrophic compressible mode is also identified in a wide range of N-rho and Pr for all eta considered, and this mode mainly occurs in the convection with relatively small Pr and large N.. The instability processes are classified into five categories. In general, for the specified wavenumber m, the parameter space (Pr, N-rho) of the fifth category, in which the base state loses stability via the quasi-geostrophic compressible mode and remains unstable, shrinks as eta increases. The asymptotic scaling behaviours of the critical Rayleigh numbers Ra-c and corresponding wavenumbers m(c) to Ta are found at different eta for the same instability mode. As eta increases, the flow stability is strengthened. Furthermore, the linearized perturbation equations and Reynolds-Orr equation are employed to quantitatively analyse the mechanical mechanisms and flow instability mechanisms of different modes. In the quasi-geostrophic compressible mode, the time-derivative term of disturbance density in the continuity equation and the diffusion term of disturbance temperature in the energy equation are found to be critical, while in the columnar and inertial modes, they can generally be ignored. Because the time-derivative term of the disturbance density in the continuity equation cannot be ignored, the anelastic approximation fails to capture the instability mode in the small-Pr and large-N-rho system, where convection onset is dominated by the quasi-geostrophic compressible mode. However, all the modes are primarily governed by the balance between the Coriolis force and the pressure gradient, based on the momentum equation. Physically, the most important difference between the quasi-geostrophic compressible mode and the columnar mode is the role played by the disturbance pressure. The disturbance pressure performs negative work for the former mode, which appears to stabilize the flow, while it destabilizes the flow for the latter mode. As eta increases, in the former mode the relative work performed by the disturbance pressure increases and in the latter mode decreases.
Pierre DegondDepartment of Mathematics, Imperial College London, London, SW7 2AZ, UKSara Merino-AceitunoDepartment of Mathematics, Imperial College London, London, SW7 2AZ, UK; Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria; Department of Mathematics, University of Sussex, Falmer, Brighton, BN1 9RH, UKFabien VergnetLaboratoire de mathématiques d’Orsay (LMO), Université Paris-Sud, CNRS, Universit Paris-Saclay, 15 rue Georges Clémenceau, 91405, Orsay Cedex, FranceHui YuInstitut für Geometrie und Praktische Mathematik, RWTH Aachen University, 52062, Aachen, Germany; Mathematical Sciences Center, Tsinghua University, Haidian District, Beijing, 100084, China
Fluid Dynamics and Shock Wavesmathscidoc:2205.14015
Journal of Mathematical Fluid Mechanics, 21, (6), 2019.1
We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek–Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery’s equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-graining we obtain a coupled Self-Organised Hydrodynamics–Stokes system. We perform a linear stability analysis for this system which shows that both pullers and pushers have unstable modes. We conclude by providing extensions of the Vicsek–Stokes model including short-distance repulsion, finite particle inertia and finite Reynolds number fluid regime.
We successfully perform the three-dimensional tracking in a turbulent fluid flow of small axisymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier-Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravitational torque stability number and by the particle aspect ratio. We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential orientation and tumbling rate of the particles. We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.
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.
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.
Shuang LiuUniversity of Science and Technology of ChinaZhenhua WanUniversity of Science and Technology of ChinaRui YanUniversity of Science and Technology of ChinaChao SunTsinghua UniversityDejun SunUniversity of Science and Technology of China
Fluid Dynamics and Shock Wavesmathscidoc:2205.14011
The onset of thermal convection in a rapidly rotating spherical shell is studied by linear stability analysis based on the fully compressible Navier-Stokes equations. Compressibility is quantified by the number of density scale heights N-rho, which measures the intensity of density stratification of the motionless, polytropic base state. The nearly adiabatic flow with polytropic index n = 1.499 < na = 1.5 is considered, where na is the adiabatic polytropic index. By investigating the stability of the base state with respect to the disturbance of specified wavenumber, the instability process is found to be sensitive to the Prandtl number Pr and to N-rho. For large Pr and small N-rho, the quasi-geostrophic columnar mode loses stability first; while for relatively small Pr a new quasi-geostrophic compressible mode is identified, which becomes unstable first under strong density stratification. The inertial mode can also occur first for relatively small Pr and a certain intensity of density stratification in the parameter range considered. Although the Rayleigh numbers Ra for the onsets of the quasi-geostrophic compressible mode and columnar mode are different by several orders of magnitude, we find that they follow very similar scaling laws with the Taylor number. The critical Ra for convection onset is found to be always positive, in contrast with previous results based on the widely used anelastic model that convection can occur at negative Ra. By evaluating the relative magnitude of the time derivative of density perturbation in the continuity equation, we show that the anelastic approximation in the present system cannot be applied in the small-Ra and large-N-rho regime.
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