Pan Xiaomin

Shanghai University | SHU · Department of Mathematics

In this study, we present a novel non-intrusive reduced-order model (ROM) for solving time-dependent stochastic partial differential equations (SPDEs). Utilizing proper orthogonal decomposition (POD), we extract spatial modes from high-fidelity solutions. A dynamic mode decomposition (DMD) method is then applied to vertically stacked matrices of pr...

This study investigates the non-Oberbeck–Boussinesq (NOB) Rayleigh–Bénard convection inside a two-dimensional rectangular cavity for a fluid with a high Prandtl number (\({\text {Pr}} = 2547.0\)). The parametric study focuses on the aspect ratio (\(\Gamma\), \(0.3\le \Gamma \le 8\)) dependence of heat transfer and fluid flows on the Rayleigh number...

In this study, we examined non-Oberbeck–Boussinesq (NOB) effects on a water-filled differentially heated vertical cavity through two-dimensional direct numerical simulations. The simulations encompassed a Rayleigh number (Ra) span of 107–1010, temperature difference (Δθ̃) up to 60 K, and a Prandtl number (Pr) fixed at 4.4. The center temperature (θ...

Non-Oberbeck–Boussinesq (NOB) effects in three representative fluids are quantitatively investigated in two-dimensional Rayleigh–Bénard convection. Numerical simulations are conducted in air, water, and glycerol with Prandtl numbers of Pr=0.71,4.4, and 2547, respectively. We consider Rayleigh number Ra∈[106,109] involving temperature difference (Δθ...

This paper presents an efficient monolithic projection-based method with staggered time discretization (MPM-STD) to examine the non-Oberbeck–Boussinesq (NOB) effects in several natural convection problems involving dramatic temperature-dependent changes in fluid properties. The proposed approach employs the Crank–Nicolson scheme along with staggere...

Direct numerical simulations of Rayleigh–Bénard convection flows are performed for Pr=0.7 with Ra=5×108 and 2×1010, and for Pr=0.021 with Ra=107 and 5×108, where Pr and Ra are the Prandtl number and the Rayleigh number, respectively. The velocity-gradient production based on the short-time averaging shows the near-wall intensive positive peak and n...

The aim of this study is to devise an efficient and scalable computational procedure to solve the many tridiagonal systems in multi-dimensional partial differential equations. The modified Thomas algorithm and a newly designed communication scheme were used to reduce the communication overhead encountered while solving the many tridiagonal systems....

We propose a non-iterative monolithic projection-based method to examine the nonlinear dynamics of time-dependent chemotaxis-driven bioconvection problems. In the proposed method, all the terms are advanced using the Crank–Nicolson scheme in time along with the second-order central difference in space. Linearizations, approximate block lower–upper...

We propose a non-intrusive reduced-oder modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides an optimally ordered basis from a set of selected full-order snapshots. Truncating this optimal basis, we constr...

For a more efficient algorithm, we introduce staggered time discretization to improve the previous method (Pan et al., 2017), fully decoupled monolithic projection method with one Poisson equation (FDMPM-1P), to solve time-dependent natural convection problems. The momentum and energy equations are discretized using the Crank–Nicolson scheme at the...

We propose a non-intrusive reduced-order modeling method based on proper orthogonal decomposition (POD) and polynomial chaos expansion (PCE) for stochastic representations in uncertainty quantification (UQ) analysis. Firstly, POD provides an optimally ordered basis from a set of selected full-order snapshots. Truncating this optimal basis, we then...

We study the temporal accuracy and stability of the velocity-components decoupled projection method (VDPM) for fully discrete incompressible Navier–Stokes equations. In particular, we investigate the effect of three formulations of the nonlinear convection term, which include the advective, skew-symmetric, and divergence forms, on the temporal accu...