The non-destructive testing of austenitic welds using ultrasound plays an important role in the assessment of the structural integrity and safety of critical structures in a nuclear reactor. The bedspring and the deck are complex welded structures of very restricted access; the ability to reliably detect and locate defects like cracks is therefore a difficult challenge. Ultrasonic testing is a well-recognized non-invasive technique which exhibits high characterization performances in homogeneous media (steel). However, its capabilities are hampered when operating in heterogeneous and anisotropic austenitic welds because of deviation and splitting of the ultrasonic beam. In order to rise to this important challenge, a model-based method is proposed, which takes into account a prior knowledge corresponding to the welding procedure specifications that condition the austenitic grains orientation within the weld and thus the wave propagation. The topological imaging method implemented is a differential approach which, compares signals from the reference defect-free medium to the inspected medium. It relies on combinations of two computed ultrasonic fields, one forward and one adjoint. Numerical simulations and experiments have been carried out to validate the practical relevance of this approach to detect and locate a flaw in a weld.