Fast Spectral Thermal Simulation for Wire Laser Additive Manufacturing

Low-latency prediction of thermal fields is essential for in-process monitoring, path planning, and defect prevention in Wire Laser Additive Manufacturing (WLAM). In this work, a fast physics-based spectral methodology for temperature monitoring and prediction in WLAM is presented. The transient heat equation with temperature-dependent properties is solved by a pseudo-spectral Fourier scheme in space and a firstorder Exponential Time Differencing (FFT-ETD1) update in time, which analytically integrates the linear diffusion in the spectral domain while the nonlinear residual (moving heat input and surface exchanges) is treated explicitly. The heat input is represented by a double-ellipsoidal (Goldak) volumetric source with energy normalization to conserve absorbed power. Boundary losses are applied with a thin-layer sink combining convectionradiation at the free surfaces and convection at the base. For process monitoring, a thermocouple (TC) and the global maximum temperature are streamed at each time step and are used in a lightweight calibration loop (Differential Evolution followed by L-BFGS-B) to align the model with in-situ data. On a representative single pass, TC and peak-temperature histories are reproduced with about $6 \%$ normalized error, indicating suitability for parameter studies and supervisory monitoring in wire-laser deposition.