Zhiyuan Sun

Zhiyuan Sun, Jun Liu, Pei Wang

We present a consistent high-order staggered Lagrangian hydrodynamics framework designed to reconcile an underlying disparity in existing curvilinear formulations: the mismatch between quadrature-based "strong" mass conservation and the discrete degrees of freedom (DOFs) of thermodynamic variables. By mathematically coupling the numerical quadrature rule with the density representation, our approach ensures rigorous point-wise consistency between density, internal energy, and pressure. This synchronization eliminates the ambiguity of equation-of-state (EOS) updates inherent in previous high-order staggered methods. To stabilize the discretization, we develop a high-order generalization of the subzonal pressure method by conceptually enriching the pressure field from the $Q^{m-1}$ to the $Q^m$ finite element space. We prove that evaluating this enriched field using a high-order quadrature rule naturally generates a restorative anti-hourglass force, which exactly recovers the classical $Q^1-P^0$ compatible hydrodynamics algorithm as a limiting case for $m=1$. Furthermore, we introduce a concise, algorithmic formulation of tensor artificial viscosity that streamlines implementation and significantly reduces computational overhead in high-order settings. The resulting framework yields strictly diagonal mass matrices for both momentum and energy equations, enabling highly efficient, fully explicit time integration without global linear solves. Extensive numerical benchmarks, including smooth convergence tests and complex shock-dominated flows, demonstrate that the proposed method achieves optimal high-order accuracy while maintaining superior geometric robustness.

Xueting Luo, Hao Deng, Jihong Yang et al.

The necessity of achieving an effective balance between minimizing the losses associated with restricting human mobility and ensuring hospital capacity has gained significant attention in the aftermath of COVID-19. Reinforcement learning (RL)-based strategies for human mobility management have recently advanced in addressing the dynamic evolution of cities and epidemics; however, they still face challenges in achieving coordinated control at the township level and adapting to cities of varying scales. To address the above issues, we propose a multi-agent RL approach that achieves Pareto optimality in managing hospital capacity and human mobility (H2-MARL), applicable across cities of different scales. We first develop a township-level infection model with online-updatable parameters to simulate disease transmission and construct a city-wide dynamic spatiotemporal epidemic simulator. On this basis, H2-MARL is designed to treat each division as an agent, with a trade-off dual-objective reward function formulated and an experience replay buffer enriched with expert knowledge built. To evaluate the effectiveness of the model, we construct a township-level human mobility dataset containing over one billion records from four representative cities of varying scales. Extensive experiments demonstrate that H2-MARL has the optimal dual-objective trade-off capability, which can minimize hospital capacity strain while minimizing human mobility restriction loss. Meanwhile, the applicability of the proposed model to epidemic control in cities of varying scales is verified, which showcases its feasibility and versatility in practical applications.