Date/Time : 04 Nov 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Li Te, National University of Singapore

Hydrodynamic stability at high Reynolds number is a central topic in fluid mechanics, which is related to turbulence. The stability of general flows and their transition are challenging problems. We develop a systematic method to establish some sharp resolvent estimates for the linearized operator around some typical shear flows and rotating flows. One of the main difficulties is that the linearized operator is non-self-adjoint and non-local such that the spectral analysis becomes very complicated. Based on the resolvent estimates, we first show the sharp enhanced dissipation rate of the solution for the linearized system. We also derive the space-time estimates of the nonlinear part using the resolvent estimates. Combining this, we obtain the nonlinear transition threshold of some typical shear flows and rotating flows.

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Date/Time : 28 Oct 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Gu Yejun, Institute of High Performance Computing, A*STAR

Abstract:  The mechanical properties of metallic materials are strongly dependent on their microstructural features (e.g. morphology and distribution of dislocations, grains, and other defects). Thus it necessitates a comprehensive understanding of the microstructure evolutions in materails during deformation. I will present some attempts of applying mathematical methods to address this problem. The presentation consists of two parts: one is the fast algorithms for solving partial differential equations, in order to precisely describe the microstructure evolutions; the other is the probabilistic description and statistical analysis, which are employed to quantify the relationship between the microstructures and mechanical properties.

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Date/Time : 30 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Huang Fukeng, National University of Singapore

Abstract: Recently it has been observed that when the interfacial tension is lower than normal liquids by two to three orders, the pinch-off dynamics is dominated by bulk diffusion [PRL 123, 134501 (2019)], showing a scaling behavior distinct from that dominated by Stokes flow. We employ the Cahn-Hilliard-Navier-Stokes model to investigate the pinch-off dynamics of a liquid thread surrounded by a viscous external fluid. A characteristic length scale is introduced to measure the competition between diffusion and viscous flow in interfacial motion. The crossover between the Stokes regime and the diffusion-dominated regime is investigated numerically and analytically to reveal how the scaling behaviors of similarity solutions are to be qualitatively changed as the characteristic length scale is accessed by the pinching neck of the interface.

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Date/Time : 23 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Nurul Huda binti Mohammad Ramli, Universiti Brunei Darussalam

Abstract: In this talk, I will discuss the methods of kernel density estimation for the estimation of particle concentrations in Lagrangian SDE trajectory models. We consider a simple two-dimensional Lagrangian model to describe the advection-diffusion flow in a chaotic advection regime. This method is chosen because the implemented numerical method to solve its Eulerian Fokker-Planck Equation provides very accurate solutions for the particle concentration, which can be used to assess our kernel density methods from the trajectory models. Some standard techniques of bandwidth selection are briefly discussed, and then a new approach using Green’s function to construct a more accurate kernel density estimator is proposed.

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Date/Time : 14 Sep 2022 16:00
Venue : S17 #06-11 (SR6)
Speaker : Zhang Huangwei, National University of Singapore

Abstract: High-fidelity numerical simulations with detailed chemistry have played significant roles not only in revealing fundamental physicochemical processes in combustion transient, but also designing next-generation propulsion systems. In this talk, an overview of development history and the state of the art of numerical combustion will be first provided. Then the hybrid Eulerian-Lagrangian method with two-way coupling is used in our studies for modelling detonation wave dynamics in two-phase gas-droplet mixture and the numerical implementations based on the open-source CFD package OpenFOAM will be introduced. We have studied hydrogen detonation transmission in fine water sprays based on the one-dimensional and two-dimensional problems. It is found that the existence of the dispersed droplets leads to varied detonation propagation modes depending on the droplet mass loading. Meanwhile, two-phase interfacial instability occurs due to the Kelvin–Helmholtz instability, arising from the pronounced velocity difference across the spray cloud boundary. Moreover, detonative combustion based on liquid n-heptane fuel is also studied. The results show that the fuel droplet heating and evaporation considerably affect detonation propagation speed, composite structure of shock and reaction front, as well as unsteady phenomena.

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Date/Time : 09 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Chen Haoyang, National University of Singapore

Abstract:  We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3$ and $H^2$, respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. In 2D, we prove the $H^11/4$ and $H^7/4$ ill-posedness for the elastic wave equations and ideal MHD system (also for Euler equations). Compared with the 3D case, the construction of ill-posed profile in 2D is more delicate. This talk is based on joint works with Xinliang An and Silu Yin.

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Date/Time : 31 Aug 2022 16:00
Venue : via Zoom
Speaker : Li Lei, Shanghai Jiao Tong University

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https://nus-sg.zoom.us/j/89214687255?pwd=VmxLYjE3MzJkTFYwdlpXa0swdWxNUT09

Meeting ID: 892 1468 7255
Passcode: 871914

Abstract:  I will give a brief introduction to our recent works regarding the applications of interacting particle systems in scientific computing. In the first part, I will talk about several algorithms we proposed for sampling and solving PDEs using interacting particle systems, which can be efficiently implemented with the random batch approximation. In particular, the random batch Monte Carlo method, the random batch Ewald method and a particle method for PNP equation will be talked about. The second part goes to the fluctuation suppression and enhancement phenomena in interacting particle systems, which may give some evidence why sampling based on particle systems may be preferred sometimes.

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Date/Time : 26 Aug 2022 10:00
Venue : S17 #06-11 (SR6)
Speaker : Zhang Junyan, National University of Singapore

Abstract: We consider 3D compressible Euler equations in a moving domain diffeomorphic to the lower-half space. The fluid is under the influence of gravity and surface tension, and not assumed to be irrotational. We prove the local well-posedness(LWP), incompressible limit(low Mach number limit) and zero surface tension limit. The proof is based on tangential-smoothing approximation and Lax-Phillips duality to establish LWP; and a carefully-chosen weighted energy to establish an estimate uniform in both Mach number and surface tension. This is the joint work with Chenyun Luo at CUHK.

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Date/Time : 18 Aug 2022 10:00
Venue : via Zoom
Speaker : Fu Zhaohui, The University of British Columbia

Abstract:  Gradient flow models attract much attention these years. The energy naturally decreases along the direction of gradient flows. In order to preserve this property, various numerical schemes have been developed and among them, the exponential time differencing Runge–Kutta method (ETDRK) and the implicit-explicit (IMEX) Runge-Kutta method are two significant approaches. In this talk we introduce these two methods and prove them to unconditionally preserve the energy dissipation law for a family of phase field models, such as the Allen–Cahn equation, the Cahn–Hilliard equation and the molecular beam epitaxy (MBE) model. Furthermore, we present some numerical experiments to demonstrate the accuracy and stability of these schemes.

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