The extent to which a three-dimensional extrusion of a two-dimensional microstructure (2DM) can reproduce the thermomechanical response of a fully three-dimensional microstructure (3DM) during laser surface scanning is investigated. A multi-physics numerical framework coupling computational thermal fluid dynamics (CFD), phase-field (PF) solidification, and thermo-elasto-viscoplastic finite element (TEVP-FE) modeling is employed to simulate a single laser line scan on a 316L stainless steel substrate. The temperature evolution obtained from CFD and the final microstructure predicted by PF simulations are used to perform two TEVP-FE simulations that differ only in the microstructure representation: 2DM and 3DM. Residual stresses, plastic strains, and Nye’s tensor are compared at both local and statistical levels. The 2DM approximation captures the overall spatial evolution trends and the order of magnitude of residual stresses, but it does not reproduce the localization of shear stresses, plastic strains, and Nye’s tensor, which is strongly influenced by the 3D grain morphology. Nevertheless, comparison of grain surface-averaged quantities on the lasered surface shows that the intergranular mechanical fields predicted by 2DM and 3DM match well in magnitudes and evolution trends. These results quantify the advantages and limitations of 2D microstructure approximations and provide guidance on the model complexity required for predicting intergranular mechanical fields at local and statistical levels.
The HLLC Riemann solver is widely used for compressible multi-medium flows, with two genuinely nonlinear waves with speeds SL and SR, and a linearly degenerate contact wave with speed S*, yet its construction relies crucially on the wave-speed ordering SL ≤ S* ≤ SR. We demonstrate that this ordering can fail for the stiffened-gas equation of state with physically admissible negative pressures, undermining existing bound-preserving (BP) analyses that assume it without verification. To address this issue, we derive a sufficient condition for the ordering and propose simple modifications to the standard Davis and Roe-average wave-speed estimates that enforce it. With these modified estimates, we prove that the HLLC solution is bound-preserving and construct a first-order finite-volume scheme with rigorous BP guarantees. Numerical experiments confirm the theoretical findings and demonstrate the robustness of the proposed approach. The modifications guarantee the ordering for a broad class of equations of state (including the stiffened-gas, van der Waals, Jones-Wilkins-Lee, and other Mie-Grüneisen) and are simple, inexpensive, and readily applicable to existing HLLC-based solvers.
We consider the problem of computing Taylor approximations to the optimal feedback law and value function for infinite-horizon finite-dimensional nonlinear optimal control problem—also known as Al'brekht's method. The scalability of existing Al'brekht-based approaches to computing approximate solutions to the Hamilton-Jacobi-Bellman equation associated with the optimal control problem has been severely limited by computational resources. The computational time issue has been partially mitigated by recent works leveraging tensor-structure to develop efficient numerical methods. However, RAM requirements still have remained a major hindrance to scaling beyond state dimensions of a few hundred or low thousands. We propose an acceleration to compute the expensive higher-order terms in a reduced space, mitigating the curse of dimensionality. A fast and scalable Matlab implementation is provided open-source for general purpose use, with the ability to accommodate arbitrary polynomial nonlinearities in the control-affine state equation, as well as polynomial state-dependence in the cost function, and the ability to handle systems in generalized form with a non-identity mass matrix, such as finite element models. Combined with the exploitation of sparsity and modern low-rank Riccati solvers, this permits computing approximations to polynomial feedback laws based on Al'brekht's method in hundreds of thousands of states.
Nowadays, human space exploration is progressing beyond low-Earth and geosynchronous orbits into far-Earth and deep-space environments. The magnetospheric dynamics in these environments are characterized by complex interactions with the solar wind, necessitating magnetohydrodynamic simulations. Recent advancements in deep learning have demonstrated the potential of physics-informed neural networks (PINNs) for solving systems of partial differential equations. However, existing PINN methods often struggle to balance multiple loss components and to tune parameters to achieve higher solution accuracy. To address these challenges, a boundary implicit-enforced PINN (BIE-PINN) architecture is proposed. Rather than designing penalty terms in the loss function to enforce boundary conditions, a synthesized field is designed, composed of a mask function, boundary-modulation functions, and boundary-profile functions. Inspired by the ghost-point method, by solving the relation between the ghost and mirror points, the boundary conditions are implicitly enforced. In this way, the convergence to the solution and the inference capability of the PINNs are enhanced. The only data required for the BIE-PINN are the initial field. The proposed BIE-PINN was validated by a one-dimensional Brio–Wu shock tube problem, a two-dimensional Orszag–Tang vortex problem. A simulation of solar wind interaction with a planet with a non-intrinsic magnetic field was carried out. The results from the BIE-PINN were compared with those from a numerical solver, demonstrating good solution accuracy and inference capability, positioning the BIE-PINN as a promising alternative for high-fidelity, fast-turnaround, global-scale magnetospheric simulations.
