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.
Tao YangTsinghua UniversityJian ChangBournemouth UniversityBo RenTsinghua UniversityMing C. LinUniversity of North Carolina at Chapel Hill Jian Jun ZhangBournemouth UniversityShi-Min HuTsinghua University
ACM Transactions on Graphics, 34, (6), 201, 2015.12
Multiple-fluid interaction is an interesting and common visual phenomenon we often observe. In this paper we present an energybased Lagrangian method that expands the capability of existing multiple-fluid methods to handle various phenomena, including extraction, partial dissolution, etc. Based on our user-adjusted Helmholtz free energy functions, the simulated fluid evolves from high-energy states to low-energy states, allowing flexible capture of various mixing and unmixing processes. We also extend the original Cahn-Hilliard equation to gain abilities of simulating complex fluid-fluid interaction and rich visual phenomena such as motionrelated mixing and position based pattern. Our approach is easy to be integrated with existing state-of-the-art smooth particle hydrodynamic (SPH) solvers and can be further implemented on top of the position based dynamics (PBD) method, improving the stability and incompressibility of the fluid during Lagrangian simulation under large time steps. Performance analysis shows that our method is at least 4 times faster than the state-of-the-art multiple-fluid method. Examples are provided to demonstrate the new capability and effectiveness of our 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.
We prove the Landau-Ginzburg/Calabi-Yau correspondence between the Gromov-Witten theory of each elliptic orbifold curve and its Fan-Jarvis-Ruan-Witten theory counterpart via modularity. We show that the correlation functions in these two enumerative theories are different representations of the same set of quasi-modular forms, expanded around different points on the upper-half plane. We relate these two representations by the Cayley transform.
Tiexiang LiDepartment of Mathematics, Southeast UniversityTsung-Ming HuangDepartment of Mathematics, National Taiwan Normal UniversityWen-Wei LinDepartment of Applied Mathematics, National Chiao Tung UniversityJenn-Nan WangInstitute of Applied Mathematics, National Taiwan University
We study a robust and efficient eigensolver for computing the positive dense spectrum of the two-dimensional transmission eigenvalue problem (TEP) which is derived from the Maxwell’s equation with complex media in pseudo-chiral model and the transverse magnetic mode. The discretized governing equations by the N ́ed ́elec edge element result in a large-scale quadratic eigenvalue problem (QEP). We estimate half of the positive eigenvalues of the QEP are on some interval which forms a dense spectrum of the QEP. The quadratic Jacobi-Davidson method with a so-called non-equivalence deflation technique is proposed to compute the dense spectrum of the QEP. Intensive numerical experiments show that our proposed method makes the convergence efficiently and robustly even it needs to compute more than 5000 desired eigenpairs. Numerical results also illustrate that the computed eigenvalue curves can be approximated by the non- linear functions which can be applied to estimate the density of the eigenvalues for the TEP.