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
[05505] Analytical solution to the elliptic PDE of shelf wave with the relaxation of semi-geostrophic approximation
Format : Talk at Waseda University
Author(s) :
Hui Wu (East China Normal University)
Abstract : The response of a wide shelf to sub-inertial and barotropic offshore pressure signals from the shelf edge was investigated. By relaxing the semi-geostrophic approximation, an elliptical wave structure equation was formulated and solved with the integral transform method. It was found that when the imposed offshore signal has an along-shelf length scale similar to the shelf width, it can efficiently break the potential vorticity barrier and propagate towards the coast, producing a significant coastal sea-level set-up. Thereafter, the pressure signal reflects from the coast or the sloping topography, producing a transient eddy and propagates to the downshelf. The intensities of the coastal set-up and the eddy increase as the along-shelf scale of the sub-inertial signal decreases or when its timescale is close to the inertial period. For a signal with longer timescale, the eddy is insignificant. The nature of the shelf response is controlled by the shelf conductivity κ≡r⁄((fsB) ), in which r is the Rayleigh friction coefficient, f is the Coriolis parameter, s is the shelf slope, and B is the shelf width, respectively. For a given offshore signal, coastal set-up increases with κ. For large κ, the eddy energy is concentrated at low modes, producing a large eddy, whereas a small κ produces a small eddy. The proposed theory can explain coastal sea-level fluctuations under eddy impingement in the Mid-Atlantic Bight or other similar areas.
[05534] Two-grid Finite Element Decoupling Scheme for the Mixed Navier-Stokes/Darcy Model
Author(s) :
Yanren Hou (Xi'an Jiaotong University)
Abstract : For the mixed steady-state Navier-Stokes/Darcy model with BJS interface condition, a two-grid FEM based decoupling scheme is analyzed in the talk. The well-posedness of the discrete system and its optimal error estimation are obtained.
[05325] On discrete shape gradients of boundary type for PDE-constrained shape optimizations
Format : Talk at Waseda University
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.
[05670] An Incremental SVD Method for integral-differential equations: Addressing Storage and Computational Challenges
Author(s) :
Yangwen Zhang (University of Louisiana at Lafayette)
Abstract : It is well known that the numerical solution of the Non-Fickian flows at the current stage depends on all previous time instances. Consequently, the storage requirement increases linearly, while the computational complexity grows quadratically with the number of time steps. This presents a significant challenge for numerical simulations, and to the best of our knowledge, it remains an unresolved issue. In this paper, we present a memory-free algorithm, based on the incremental SVD technique, that exhibits only linear growth in computational complexity as the number of time steps increases. We prove that the error between the solutions generated by the conventional algorithm and our innovative approach lies within the scope of machine error. Numerical experiments are showcased to affirm the accuracy and efficiency gains in terms of both memory usage and computational expenses.
[05596] An incremental SVD method for integro-differential equations: addressing storage and computational challenges
Format : Online Talk on Zoom
Author(s) :
Yangwen Zhang (University of Louisiana at Lafayette)
Gang Chen (Sichuan University)
Abstract : At the current stage, it is widely recognized that the numerical solution of integro-differential equations with a memory term depends on all previous time instances. Consequently, the storage requirement increases linearly, while the computational complexity grows quadratically with the number of time steps. This presents a significant challenge for numerical simulations, and to the best of our knowledge, it remains an unresolved issue. In this paper, we present a memory-free algorithm, based on the incremental SVD technique, that exhibits only linear growth in computational complexity as the number of time steps increases. Rigorous error analysis and numerical experiments will be presented to validate our approach.
[02217] Parameterizing the baroclinic instability with an artificial potential energy term
Format : Online Talk on Zoom
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.
[05568] Boundary layer dynamics of wave-current flows over cylindrical canopies
Format : Talk at Waseda University
Author(s) :
Jun Ao Kan (Shanghai Jiao Tong University)
Rui Wang (Shanghai Jiao Tong University)
Hui Xu (Shanghai Jiao Tong University)
Abstract : Interactions of waves and currents with large roughness elements in the coastal ocean play a crucial role in drag generation and energy dissipation, which are quite different from the extensively-investigated smooth wall boundary layer or small-scale roughness. In the framework of high-order spectral/hp element method, the present study focuses on the analysis of implicit large eddy simulations of the combined current-wave flows over arrays of staggered circular cylinders with a diameter and a height of 0.5D. Unlike previous studies, our research examines array units that go beyond individual obstacles, enabling us to explore a wider range of physical mechanisms in turbulence, which consequently increases the computational complexity. By manipulating the wave amplitude, three distinct scenarios were obtained (i.e. pure current, weak wave and strong wave conditions, respectively) to analyze the effects of waves on currents or vice versa. The primary objective of current work is to investigate the energy transport mechanisms between the canopy and non-canopy layers, as well as the characteristics of the population of coherent structures. The dependences of energy budget, large-scale structures, sweeps and ejections are analyzed in detail.
[05525] Shape Optimization of Incompressible Navier-Stokes flows with Shape Gradients
Format : Talk at Waseda University
Author(s) :
Shengfeng Zhu (East China Normal University)
Jiajie Li (East China Normal University)
Abstract : Shape design of fluid flows has applications in engineering. We consider shape optimization of incompressible flows with shape gradients. Traditional boundary shape gradients have high smoothness requirement on the boundary and is less general than the distributed shape gradient. We consider numerically finite element approximations to the distributed and boundary corrected shape gradients. A prior error estimates are shown. Numerical results are reported to verify theory and show effectiveness of shape gradient algorithms.
[05546] Causal AI Ocean Learning and Prediction
Author(s) :
X. San Liang (Fudan University)
Abstract : Ocean-atmosphere forecasting is faced with many challenges such as open boundary condition specification, unresolved process parameterization, unknown physics modeling, etc. Even if all these are fixed, a more challenging issue that ever exists is the unpredictability intrinsically embedded in chaotic systems. The recent fast development of AI seems to be promising for a partial solution to these problems. But AI is also faced with the problem of interpretability. Due to the black-box nature, it is difficult for one to decide whether a forecast is acceptable or not. In this presentation, I will show how interpretability will be enhanced for AI algorithms with the aid of a recently developed causality analysis which has been rigorously established from first principles during the past 18 years (e.g., Liang, Information flow and causality as rigorous physical notions ab initio. Phys Rev E 94:052201, 2016). In the oceanographic context, this is easily understood as the tracing of predictability sources to make the maximal usage of information. Also the quantitative nature of the causality analysis allows for an adjustment of the neural network to remove spurious correlations toward an optimal performance. Demonstrated here will be an operational forecast of the surface circulation of a region in the South China Sea, and a decadal forecast of the Central Pacific-type El Niño.
[03963] Simulation of Droplet-laden Turbulent Channel flow by LBM and Phase field method
Format : Online Talk on Zoom
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.
