arXiv subjects

Zhongjing Wang

Publications and source records attributed to Zhongjing Wang.

4 recordsLinked to original sources

arXiv2026

Sediment Concentration Estimation via Multiscale Inverse Problem and Stochastic Homogenization

We develop a multiscale framework for estimating sediment concentration in water flow from acoustic wave measurements. At the microscopic scale, the sediment distribution is modeled by a spatially inhomogeneous Poisson cloud, while the quantity of interest is its macroscopic concentration. For the associated random wave model, we derive an effective medium whose coefficient is explicitly related to the local probability of sediment occurrence. This effective description avoids resolving individual sediment particles and provides a computationally tractable forward model for inversion. We then formulate the recovery of the effective medium, and hence the sediment concentration, as an inverse medium problem from partial boundary measurements, and investigate numerical strategies including model mollification and shot averaging. Numerical experiments demonstrate that the effective model captures the macroscopic wave behavior and can be used to obtain accurate estimates of sediment concentration.

math.NA↗

arXiv2025

An Acoustic Inversion-Based Flow Measurement Model in 3D Hydrodynamic Systems

This study extends the flow measurement method initially proposed in [22] to three-dimensional scenarios, addressing the growing need for accurate and efficient non-contact flow measurement techniques in complex hydrodynamic environments. Compared to conventional Acoustic Doppler Current Profilers (ADCPs) and remote sensing-based flow monitoring, the proposed method enables high-resolution, continuous water velocity measurement, making it well-suited for hazardous environments such as floods, strong currents, and sediment-laden rivers. Building upon the original approach, we develop an enhanced model that incorporates multiple emission directions and flexible configurations of receivers. These advancements improve the adaptability and accuracy of the method when applied to three-dimensional flow fields. To evaluate its feasibility, we conducted extensive numerical simulations designed to mimic real-world hydrodynamic conditions. The results demonstrate that the proposed method effectively handles diverse and complex flow field configurations, highlighting its potential for practical applications in water resource management and hydraulic engineering.

math.NA↗

arXiv2023

Traceability of Water Pollution: An Inversion Scheme Via Dynamic Complex Geometrical Optics Solutions

We investigate the identification of the time-dependent source term in the diffusion equation using boundary measurements. This facilitates tracing back the origins of environmental pollutants. Employing the concept of dynamic complex geometrical optics (CGO) solutions, a variational formulation of the inverse source problem is analyzed, leading to a proof of uniqueness result. Our proposed two-step reconstruction algorithm first determines the point source locations and subsequently reconstructs the Fourier components of the emission concentration functions. Numerical experiments on simulated data are conducted. The results demonstrate that the proposed two-step reconstruction algorithm can reliably reconstruct multiple point sources and accurately reconstruct the emission concentration functions. Additionally, by partitioning the algorithm into online and offline computations, and concentrating computational demand offline, real-time pollutant traceability becomes feasible. This method, applicable in various fields - especially those related to water pollution, can identify the source of a contaminant in the environment, thus serving as a valuable tool in environmental protection.

math.NA↗

arXiv2022

Flow Measurement: An Inverse Problem Formulation

This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we formulate an inverse source problem that can recover the flow field from the observation data on a few boundary receivers. To our knowledge, this is the first mathematical model of flow measurement using partial differential equations. This model is proved well-posed, and the corresponding algorithm is derived to compute the velocity field efficiently. Extensive numerical simulations are performed to demonstrate the accuracy and robustness of our model. Our formulation is capable of simulating a variety of practical measurement scenarios.

math.OC↗