The GBS code (Ricci et al 2012 Plasma Phys. Control Fusion 54 124047) for boundary plasma turbulence is extended to handle flexible first wall geometry. This capability is enabled by the use of a finite difference scheme on a curvilinear structured grid. Grid generation and optimization leverage a spline-based elliptic grid generation framework originally developed in the context of isogeometric analysis applications (Hinz and Buffa 2024 Eng. Comput. 40, 3735-3764). First turbulence simulations of the Tokamak à Configuration Variable with a realistic first wall geometry including baffles are presented and highlight a reduction of upstream fluctuations compared to unbaffled cases.