<p>Different modeling approaches namely, Eulerian (CFD model), Lagrangian (CSM model), and Arbitrary Lagrangian–Eulerian (ALE model) were developed to study the complex and nonlinear interactions of thermal, mechanical and material flow phenomena during the Friction stir butt welding (FSBW) of 6&#xa0;mm thick precipitation-hardened Al–Cu binary alloy (AA2219-T87) plates with a conical tool-pin. Overall predictions by the individual models were discussed in terms of thermal and material flow fields, size of weld zones, shear strain rates, flow stresses and workpiece deformation. Further, the accuracy of individual models was tested by comparing the predicted weld zones with the experiments. Since the individual CFD and CSM models do not account for the real-time interfacial boundary conditions between the plasticized workpiece material and rigid tool motion, the predicted weld zones don't agree with the experiments. ALE model combines the benefits and overcomes the deficiencies of CFD and CSM models, and hence the predicted weld zones and workpiece deformation were found to be in good agreement with the experiments. Therefore, the authors strongly recommend to use the ALE model and optimize the process and tool parameters (tool’s rotational and traverse speeds, tool shoulder and pin diameters, etc.) instead of the trials based expensive physical experiments.</p> Graphical abstract <p>Figs. Predicted fields;¹thermal,²material flow,³material deformation</p>