Auto-Differentiable Locally-Conservative Transport Solver for Designing Tritium Breeders
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In this presentation, we introduce a locally conservative scalar transport solver with auto-differentiability to design tritium breeders, which is an essential component to achieve self-sustainable fusion energy generation. We consider a domain consists of porous material and pure void. Neutron bombardment of the material generates tritium atoms, which diffuse through the pore network to reach the pure void space and are extracted by flowing helium. Traditional pebble-bed designs with randomly packed spheres results in slow flow velocity and large pumping power loss, which is inefficient for tritium recovery. We solve this advection-diffusion-reaction system using local discontinuous Galerkin (LDG) method to enforce total flux continuity strongly across the material-void interface that marks the sharp transition from diffusion-dominated to advection-dominated regime. The strong flux continuity ensures local mass conservation and thus prevents numerical oscillations in the solution, even when incompressibility is weakly imposed in the velocity field. The LDG method introduces an auxiliary diffusive flux variable and results in a saddle-point block system, which is resolved efficiently with an approximate Schur complement block preconditioner. By coupling the transport solver with pressure correction incompressible Navier-Stokes flow solver, we first predict tritium breeding rate of various architectures, such as gyroids and woodpile lattices, and compare the performance against the traditional pebble-bed design. Afterwards, we conduct shape optimization to further enhance the breeding rate.
