Haroon Ahmad | Searcharxiv

arXiv2026

Oscillatory liquid-metal flow in a channel under rapidly decaying applied magnetic field

The channel flow of a liquid metal driven by a rapidly varying applied magnetic field is analyzed. The flow configuration, physical properties, and parameters correspond to a duct within a liquid-metal blanket of a nuclear fusion reactor under off-normal plasma conditions, such as plasma disruptions. The problem is solved numerically using a one-dimensional flow approximation. The longitudinal magnetic field, decaying at a typical rate on the order of 100 T/s, induces eddy currents that interact with a steady wall-normal magnetic field, generating the Lorentz force that drives the flow. Standing Alfv\'en waves are identified as the key mechanism controlling the liquid metal's response. These waves manifest as large-amplitude, gradually decaying oscillations of velocity, the induced magnetic field, and eddy currents. A parametric study predicts a severe response developing within the first few milliseconds of the event, with maximum flow velocities reaching several meters per second and Lorentz forces exceeding $10^9 \text{ N/m}^3$. Power-law approximations for the dependencies of the response characteristics on the flow parameters are developed. Finally, the effects of fluid compressibility and pressure waves are analyzed and found not to lead to a major modification of the flow evolution.

physics.flu-dyn↗

arXiv2023

eXtended Hybridizable Discontinous Galerkin (X-HDG) Method for Linear Convection-Diffusion Equations on Unfitted Domains

In this work, we propose a novel strategy for the numerical solution of linear convection diffusion equation (CDE) over unfitted domains. In the proposed numerical scheme, strategies from high order Hybridized Discontinuous Galerkin method and eXtended Finite Element method is combined with the level set definition of the boundaries. The proposed scheme and hence, is named as eXtended Hybridizable Discontinuous Galerkin (XHDG) method. In this regard, the Hybridizable Discontinuous Galerkin (HDG) method is eXtended to the unfitted domains; i.e, the computational mesh does not need to fit to the domain boundary; instead, the boundary is defined by a level set function and cuts through the background mesh arbitrarily. The original unknown structure of HDG and its hybrid nature ensuring the local conservation of fluxes is kept, while developing a modified bilinear form for the elements cut by the boundary. At every cut element, an auxiliary nodal trace variable on the boundary is introduced, which is eliminated afterwards while imposing the boundary conditions. Both stationary and time dependent CDEs are studied over a range of flow regimes from diffusion to convection dominated; using high order $(p \leq 4)$ XHDG through benchmark numerical examples over arbitrary unfitted domains. Results proved that XHDG inherits optimal $(p + 1)$ and super $(p + 2)$ convergence properties of HDG while removing the fitting mesh restriction.

math.NA↗