[01003] Mathematical Modeling and Simulation in Land-Ocean Transition Zones
Session Date & Time :
01003 (1/3) : 4E (Aug.24, 17:40-19:20)
01003 (2/3) : 5B (Aug.25, 10:40-12:20)
01003 (3/3) : 5C (Aug.25, 13:20-15:00)
Type : Proposal of Minisymposium
Abstract : Around 30% of global populations live in coastal zones, which are facing increasing threatens from both land and ocean. These include saltwater intrusion, storm surge, ecosystem degeneration and coastal erosion, to name a few. Mathematical modeling and simulation on multiple processes in the land-ocean transition zones are essential to understand intrinsic mechanisms and make reliable predictions for the future. This symposium aims to exchange new advances on mathematical modeling, numerical simulation, operational applications, and other relevant topics in hydrodynamic, ecological, and other processes in the land-ocean transition zones, thus to promote interdisciplinary collaborations in applied mathematics and earth science.
Organizer(s) : Dong Ye, Hui Wu, Hairong Yuan, Shengfeng Zhu
Shiqiu Peng (South China Sea Institute of Oceanology, CAS)
Qingshan Chen (Clemson University)
Yanren Hou (Xi’an Jiaotong University)
Gianmarco Mengaldo (National University of Singapore)
Spencer J. Sherwin (Imperial College London)
Wei Gong (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Hui Xu (Shanghai Jiao Tong University)
Yangwen Zhang (Carnegie Mellon University)
Dingyi Pan (Zhejiang University )
Shengfeng Zhu (East China Normal University)
Talks in Minisymposium :
[02217] Parameterizing the baroclinic instability with an artificial potential energy term
Author(s) :
Qingshan Chen (Clemson University)
Abstract : In a numerical model that is under-resolved in the horizontal and/or vertical directions, baroclinic instability is often
suppressed, leading to a build-up of layer interface slopes and potential energy that can not be released. In this work, we demonstrate, within the multilayer shallow water model and the Hamiltonian framework, how the baroclinic
instability can be parameterized by adding an artificial potential energy term based on the slope of the interior layer
interfaces.
[03963] Simulation of Droplet-laden Turbulent Channel flow by LBM and Phase field method
Author(s) :
Dingyi Pan (Zhejiang University)
Yuqing Lin (Zhejiang University)
Abstract : Direct numerical simulation of droplet-laden turbulent channel flow is studied by coupled lattice Boltzmann method and phase field modeling with Cahn-Hilliard (CH) equation. The weighted essentially non-oscillatory (WENO) scheme is applied for the discretization of CH equation. The simulated friction Reynolds number is up to 180, and the mass conservation of droplet phase is well fulfilled. The results show that the existence of droplets contribute to the drag reduction of the turbulent channel flow.
[05325] On discrete shape gradients of boundary type for PDE-constrained shape optimizations
Author(s) :
Wei Gong (Academy of Mathematics and Systems Science, Chinese Academy of Sciences)
Abstract : Shape gradients have been widely used in numerical shape gradient descent algorithms for shape optimization. The two types of shape gradients, i.e., the distributed one and the boundary type, are equivalent at the continuous level but exhibit different numerical behaviors after finite element discretization. To be more specific, the boundary type shape gradient is more popular in practice due to its concise formulation and convenience in combining with shape optimization algorithms but has lower numerical accuracy. In this talk we provide a simple yet useful boundary correction for the normal derivatives of the state and adjoint equations, motivated by their continuous variational forms, to increase the accuracy and possible effectiveness of the boundary shape gradient in PDE-constrained shape optimization. We consider particularly the state equation with Dirichlet boundary conditions and provide a preliminary error estimate for the correction. Numerical results show that the corrected boundary type shape gradient has comparable accuracy to that of the distributed one. Extensions to other type of PDE-constrained shape optimizations are also considered, including the interface identification problems, the eigenvalue problems, the Stokes and Navier-Stokes problems. Moreover, we give a theoretical explanation for the comparable numerical accuracy of the boundary type shape gradient with that of the distributed shape gradient for Neumann boundary value problems.
